\contentsline {chapter}{\numberline {1}\leavevmode {\color {Chapter }Introduction}}{10}{chapter.1}
\contentsline {section}{\numberline {1.1}\leavevmode {\color {Chapter }Introduction to the \textsf {GUAVA} package}}{10}{section.1.1}
\contentsline {section}{\numberline {1.2}\leavevmode {\color {Chapter }Installing \textsf {GUAVA}}}{10}{section.1.2}
\contentsline {section}{\numberline {1.3}\leavevmode {\color {Chapter }Loading \textsf {GUAVA}}}{11}{section.1.3}
\contentsline {chapter}{\numberline {2}\leavevmode {\color {Chapter }Coding theory functions in \textsf {GAP}}}{12}{chapter.2}
\contentsline {section}{\numberline {2.1}\leavevmode {\color {Chapter } Distance functions }}{12}{section.2.1}
\contentsline {subsection}{\numberline {2.1.1}\leavevmode {\color {Chapter }AClosestVectorCombinationsMatFFEVecFFE}}{12}{subsection.2.1.1}
\contentsline {subsection}{\numberline {2.1.2}\leavevmode {\color {Chapter }AClosestVectorComb..MatFFEVecFFECoords}}{13}{subsection.2.1.2}
\contentsline {subsection}{\numberline {2.1.3}\leavevmode {\color {Chapter }DistancesDistributionMatFFEVecFFE}}{13}{subsection.2.1.3}
\contentsline {subsection}{\numberline {2.1.4}\leavevmode {\color {Chapter }DistancesDistributionVecFFEsVecFFE}}{14}{subsection.2.1.4}
\contentsline {subsection}{\numberline {2.1.5}\leavevmode {\color {Chapter }WeightVecFFE}}{14}{subsection.2.1.5}
\contentsline {subsection}{\numberline {2.1.6}\leavevmode {\color {Chapter }DistanceVecFFE}}{14}{subsection.2.1.6}
\contentsline {section}{\numberline {2.2}\leavevmode {\color {Chapter } Other functions }}{15}{section.2.2}
\contentsline {subsection}{\numberline {2.2.1}\leavevmode {\color {Chapter }ConwayPolynomial}}{15}{subsection.2.2.1}
\contentsline {subsection}{\numberline {2.2.2}\leavevmode {\color {Chapter }RandomPrimitivePolynomial}}{15}{subsection.2.2.2}
\contentsline {chapter}{\numberline {3}\leavevmode {\color {Chapter }Codewords}}{17}{chapter.3}
\contentsline {section}{\numberline {3.1}\leavevmode {\color {Chapter }Construction of Codewords}}{18}{section.3.1}
\contentsline {subsection}{\numberline {3.1.1}\leavevmode {\color {Chapter }Codeword}}{18}{subsection.3.1.1}
\contentsline {subsection}{\numberline {3.1.2}\leavevmode {\color {Chapter }CodewordNr}}{19}{subsection.3.1.2}
\contentsline {subsection}{\numberline {3.1.3}\leavevmode {\color {Chapter }IsCodeword}}{20}{subsection.3.1.3}
\contentsline {section}{\numberline {3.2}\leavevmode {\color {Chapter }Comparisons of Codewords}}{20}{section.3.2}
\contentsline {subsection}{\numberline {3.2.1}\leavevmode {\color {Chapter }=}}{20}{subsection.3.2.1}
\contentsline {section}{\numberline {3.3}\leavevmode {\color {Chapter }Arithmetic Operations for Codewords}}{21}{section.3.3}
\contentsline {subsection}{\numberline {3.3.1}\leavevmode {\color {Chapter }+}}{21}{subsection.3.3.1}
\contentsline {subsection}{\numberline {3.3.2}\leavevmode {\color {Chapter }-}}{21}{subsection.3.3.2}
\contentsline {subsection}{\numberline {3.3.3}\leavevmode {\color {Chapter }+}}{21}{subsection.3.3.3}
\contentsline {section}{\numberline {3.4}\leavevmode {\color {Chapter } Functions that Convert Codewords to Vectors or Polynomials }}{22}{section.3.4}
\contentsline {subsection}{\numberline {3.4.1}\leavevmode {\color {Chapter }VectorCodeword}}{22}{subsection.3.4.1}
\contentsline {subsection}{\numberline {3.4.2}\leavevmode {\color {Chapter }PolyCodeword}}{22}{subsection.3.4.2}
\contentsline {section}{\numberline {3.5}\leavevmode {\color {Chapter } Functions that Change the Display Form of a Codeword }}{23}{section.3.5}
\contentsline {subsection}{\numberline {3.5.1}\leavevmode {\color {Chapter }TreatAsVector}}{23}{subsection.3.5.1}
\contentsline {subsection}{\numberline {3.5.2}\leavevmode {\color {Chapter }TreatAsPoly}}{23}{subsection.3.5.2}
\contentsline {section}{\numberline {3.6}\leavevmode {\color {Chapter } Other Codeword Functions }}{24}{section.3.6}
\contentsline {subsection}{\numberline {3.6.1}\leavevmode {\color {Chapter }NullWord}}{24}{subsection.3.6.1}
\contentsline {subsection}{\numberline {3.6.2}\leavevmode {\color {Chapter }DistanceCodeword}}{24}{subsection.3.6.2}
\contentsline {subsection}{\numberline {3.6.3}\leavevmode {\color {Chapter }Support}}{24}{subsection.3.6.3}
\contentsline {subsection}{\numberline {3.6.4}\leavevmode {\color {Chapter }WeightCodeword}}{25}{subsection.3.6.4}
\contentsline {chapter}{\numberline {4}\leavevmode {\color {Chapter }Codes}}{26}{chapter.4}
\contentsline {section}{\numberline {4.1}\leavevmode {\color {Chapter }Comparisons of Codes}}{28}{section.4.1}
\contentsline {subsection}{\numberline {4.1.1}\leavevmode {\color {Chapter }=}}{28}{subsection.4.1.1}
\contentsline {section}{\numberline {4.2}\leavevmode {\color {Chapter } Operations for Codes }}{29}{section.4.2}
\contentsline {subsection}{\numberline {4.2.1}\leavevmode {\color {Chapter }+}}{29}{subsection.4.2.1}
\contentsline {subsection}{\numberline {4.2.2}\leavevmode {\color {Chapter }*}}{29}{subsection.4.2.2}
\contentsline {subsection}{\numberline {4.2.3}\leavevmode {\color {Chapter }*}}{29}{subsection.4.2.3}
\contentsline {subsection}{\numberline {4.2.4}\leavevmode {\color {Chapter }InformationWord}}{30}{subsection.4.2.4}
\contentsline {section}{\numberline {4.3}\leavevmode {\color {Chapter } Boolean Functions for Codes }}{30}{section.4.3}
\contentsline {subsection}{\numberline {4.3.1}\leavevmode {\color {Chapter }in}}{30}{subsection.4.3.1}
\contentsline {subsection}{\numberline {4.3.2}\leavevmode {\color {Chapter }IsSubset}}{31}{subsection.4.3.2}
\contentsline {subsection}{\numberline {4.3.3}\leavevmode {\color {Chapter }IsCode}}{31}{subsection.4.3.3}
\contentsline {subsection}{\numberline {4.3.4}\leavevmode {\color {Chapter }IsLinearCode}}{31}{subsection.4.3.4}
\contentsline {subsection}{\numberline {4.3.5}\leavevmode {\color {Chapter }IsCyclicCode}}{31}{subsection.4.3.5}
\contentsline {subsection}{\numberline {4.3.6}\leavevmode {\color {Chapter }IsPerfectCode}}{32}{subsection.4.3.6}
\contentsline {subsection}{\numberline {4.3.7}\leavevmode {\color {Chapter }IsMDSCode}}{32}{subsection.4.3.7}
\contentsline {subsection}{\numberline {4.3.8}\leavevmode {\color {Chapter }IsSelfDualCode}}{33}{subsection.4.3.8}
\contentsline {subsection}{\numberline {4.3.9}\leavevmode {\color {Chapter }IsSelfOrthogonalCode}}{33}{subsection.4.3.9}
\contentsline {subsection}{\numberline {4.3.10}\leavevmode {\color {Chapter }IsSelfComplementaryCode}}{33}{subsection.4.3.10}
\contentsline {subsection}{\numberline {4.3.11}\leavevmode {\color {Chapter }IsAffineCode}}{34}{subsection.4.3.11}
\contentsline {subsection}{\numberline {4.3.12}\leavevmode {\color {Chapter }IsAlmostAffineCode}}{34}{subsection.4.3.12}
\contentsline {section}{\numberline {4.4}\leavevmode {\color {Chapter } Equivalence and Isomorphism of Codes }}{35}{section.4.4}
\contentsline {subsection}{\numberline {4.4.1}\leavevmode {\color {Chapter }IsEquivalent}}{35}{subsection.4.4.1}
\contentsline {subsection}{\numberline {4.4.2}\leavevmode {\color {Chapter }CodeIsomorphism}}{35}{subsection.4.4.2}
\contentsline {subsection}{\numberline {4.4.3}\leavevmode {\color {Chapter }AutomorphismGroup}}{35}{subsection.4.4.3}
\contentsline {subsection}{\numberline {4.4.4}\leavevmode {\color {Chapter }PermutationAutomorphismGroup}}{36}{subsection.4.4.4}
\contentsline {section}{\numberline {4.5}\leavevmode {\color {Chapter } Domain Functions for Codes }}{37}{section.4.5}
\contentsline {subsection}{\numberline {4.5.1}\leavevmode {\color {Chapter }IsFinite}}{37}{subsection.4.5.1}
\contentsline {subsection}{\numberline {4.5.2}\leavevmode {\color {Chapter }Size}}{37}{subsection.4.5.2}
\contentsline {subsection}{\numberline {4.5.3}\leavevmode {\color {Chapter }LeftActingDomain}}{37}{subsection.4.5.3}
\contentsline {subsection}{\numberline {4.5.4}\leavevmode {\color {Chapter }Dimension}}{37}{subsection.4.5.4}
\contentsline {subsection}{\numberline {4.5.5}\leavevmode {\color {Chapter }AsSSortedList}}{38}{subsection.4.5.5}
\contentsline {section}{\numberline {4.6}\leavevmode {\color {Chapter } Printing and Displaying Codes }}{38}{section.4.6}
\contentsline {subsection}{\numberline {4.6.1}\leavevmode {\color {Chapter }Print}}{38}{subsection.4.6.1}
\contentsline {subsection}{\numberline {4.6.2}\leavevmode {\color {Chapter }String}}{39}{subsection.4.6.2}
\contentsline {subsection}{\numberline {4.6.3}\leavevmode {\color {Chapter }Display}}{39}{subsection.4.6.3}
\contentsline {subsection}{\numberline {4.6.4}\leavevmode {\color {Chapter }DisplayBoundsInfo}}{40}{subsection.4.6.4}
\contentsline {section}{\numberline {4.7}\leavevmode {\color {Chapter } Generating (Check) Matrices and Polynomials }}{40}{section.4.7}
\contentsline {subsection}{\numberline {4.7.1}\leavevmode {\color {Chapter }GeneratorMat}}{40}{subsection.4.7.1}
\contentsline {subsection}{\numberline {4.7.2}\leavevmode {\color {Chapter }CheckMat}}{41}{subsection.4.7.2}
\contentsline {subsection}{\numberline {4.7.3}\leavevmode {\color {Chapter }GeneratorPol}}{41}{subsection.4.7.3}
\contentsline {subsection}{\numberline {4.7.4}\leavevmode {\color {Chapter }CheckPol}}{42}{subsection.4.7.4}
\contentsline {subsection}{\numberline {4.7.5}\leavevmode {\color {Chapter }RootsOfCode}}{42}{subsection.4.7.5}
\contentsline {section}{\numberline {4.8}\leavevmode {\color {Chapter } Parameters of Codes }}{42}{section.4.8}
\contentsline {subsection}{\numberline {4.8.1}\leavevmode {\color {Chapter }WordLength}}{42}{subsection.4.8.1}
\contentsline {subsection}{\numberline {4.8.2}\leavevmode {\color {Chapter }Redundancy}}{43}{subsection.4.8.2}
\contentsline {subsection}{\numberline {4.8.3}\leavevmode {\color {Chapter }MinimumDistance}}{43}{subsection.4.8.3}
\contentsline {subsection}{\numberline {4.8.4}\leavevmode {\color {Chapter }MinimumDistanceLeon}}{44}{subsection.4.8.4}
\contentsline {subsection}{\numberline {4.8.5}\leavevmode {\color {Chapter }DecreaseMinimumDistanceUpperBound}}{45}{subsection.4.8.5}
\contentsline {subsection}{\numberline {4.8.6}\leavevmode {\color {Chapter }MinimumDistanceRandom}}{45}{subsection.4.8.6}
\contentsline {subsection}{\numberline {4.8.7}\leavevmode {\color {Chapter }CoveringRadius}}{47}{subsection.4.8.7}
\contentsline {subsection}{\numberline {4.8.8}\leavevmode {\color {Chapter }SetCoveringRadius}}{48}{subsection.4.8.8}
\contentsline {section}{\numberline {4.9}\leavevmode {\color {Chapter } Distributions }}{48}{section.4.9}
\contentsline {subsection}{\numberline {4.9.1}\leavevmode {\color {Chapter }MinimumWeightWords}}{48}{subsection.4.9.1}
\contentsline {subsection}{\numberline {4.9.2}\leavevmode {\color {Chapter }WeightDistribution}}{49}{subsection.4.9.2}
\contentsline {subsection}{\numberline {4.9.3}\leavevmode {\color {Chapter }InnerDistribution}}{49}{subsection.4.9.3}
\contentsline {subsection}{\numberline {4.9.4}\leavevmode {\color {Chapter }DistancesDistribution}}{49}{subsection.4.9.4}
\contentsline {subsection}{\numberline {4.9.5}\leavevmode {\color {Chapter }OuterDistribution}}{50}{subsection.4.9.5}
\contentsline {section}{\numberline {4.10}\leavevmode {\color {Chapter } Decoding Functions }}{50}{section.4.10}
\contentsline {subsection}{\numberline {4.10.1}\leavevmode {\color {Chapter }Decode}}{50}{subsection.4.10.1}
\contentsline {subsection}{\numberline {4.10.2}\leavevmode {\color {Chapter }Decodeword}}{51}{subsection.4.10.2}
\contentsline {subsection}{\numberline {4.10.3}\leavevmode {\color {Chapter }GeneralizedReedSolomonDecoderGao}}{52}{subsection.4.10.3}
\contentsline {subsection}{\numberline {4.10.4}\leavevmode {\color {Chapter }GeneralizedReedSolomonListDecoder}}{53}{subsection.4.10.4}
\contentsline {subsection}{\numberline {4.10.5}\leavevmode {\color {Chapter }BitFlipDecoder}}{53}{subsection.4.10.5}
\contentsline {subsection}{\numberline {4.10.6}\leavevmode {\color {Chapter }NearestNeighborGRSDecodewords}}{54}{subsection.4.10.6}
\contentsline {subsection}{\numberline {4.10.7}\leavevmode {\color {Chapter }NearestNeighborDecodewords}}{55}{subsection.4.10.7}
\contentsline {subsection}{\numberline {4.10.8}\leavevmode {\color {Chapter }Syndrome}}{56}{subsection.4.10.8}
\contentsline {subsection}{\numberline {4.10.9}\leavevmode {\color {Chapter }SyndromeTable}}{56}{subsection.4.10.9}
\contentsline {subsection}{\numberline {4.10.10}\leavevmode {\color {Chapter }StandardArray}}{57}{subsection.4.10.10}
\contentsline {subsection}{\numberline {4.10.11}\leavevmode {\color {Chapter }PermutationDecode}}{57}{subsection.4.10.11}
\contentsline {subsection}{\numberline {4.10.12}\leavevmode {\color {Chapter }PermutationDecodeNC}}{58}{subsection.4.10.12}
\contentsline {chapter}{\numberline {5}\leavevmode {\color {Chapter }Generating Codes}}{59}{chapter.5}
\contentsline {section}{\numberline {5.1}\leavevmode {\color {Chapter } Generating Unrestricted Codes }}{59}{section.5.1}
\contentsline {subsection}{\numberline {5.1.1}\leavevmode {\color {Chapter }ElementsCode}}{59}{subsection.5.1.1}
\contentsline {subsection}{\numberline {5.1.2}\leavevmode {\color {Chapter }HadamardCode}}{60}{subsection.5.1.2}
\contentsline {subsection}{\numberline {5.1.3}\leavevmode {\color {Chapter }ConferenceCode}}{60}{subsection.5.1.3}
\contentsline {subsection}{\numberline {5.1.4}\leavevmode {\color {Chapter }MOLSCode}}{61}{subsection.5.1.4}
\contentsline {subsection}{\numberline {5.1.5}\leavevmode {\color {Chapter }RandomCode}}{62}{subsection.5.1.5}
\contentsline {subsection}{\numberline {5.1.6}\leavevmode {\color {Chapter }NordstromRobinsonCode}}{62}{subsection.5.1.6}
\contentsline {subsection}{\numberline {5.1.7}\leavevmode {\color {Chapter }GreedyCode}}{62}{subsection.5.1.7}
\contentsline {subsection}{\numberline {5.1.8}\leavevmode {\color {Chapter }LexiCode}}{63}{subsection.5.1.8}
\contentsline {section}{\numberline {5.2}\leavevmode {\color {Chapter } Generating Linear Codes }}{63}{section.5.2}
\contentsline {subsection}{\numberline {5.2.1}\leavevmode {\color {Chapter }GeneratorMatCode}}{63}{subsection.5.2.1}
\contentsline {subsection}{\numberline {5.2.2}\leavevmode {\color {Chapter }CheckMatCodeMutable}}{64}{subsection.5.2.2}
\contentsline {subsection}{\numberline {5.2.3}\leavevmode {\color {Chapter }CheckMatCode}}{64}{subsection.5.2.3}
\contentsline {subsection}{\numberline {5.2.4}\leavevmode {\color {Chapter }HammingCode}}{65}{subsection.5.2.4}
\contentsline {subsection}{\numberline {5.2.5}\leavevmode {\color {Chapter }ReedMullerCode}}{65}{subsection.5.2.5}
\contentsline {subsection}{\numberline {5.2.6}\leavevmode {\color {Chapter }AlternantCode}}{65}{subsection.5.2.6}
\contentsline {subsection}{\numberline {5.2.7}\leavevmode {\color {Chapter }GoppaCode}}{66}{subsection.5.2.7}
\contentsline {subsection}{\numberline {5.2.8}\leavevmode {\color {Chapter }GeneralizedSrivastavaCode}}{66}{subsection.5.2.8}
\contentsline {subsection}{\numberline {5.2.9}\leavevmode {\color {Chapter }SrivastavaCode}}{67}{subsection.5.2.9}
\contentsline {subsection}{\numberline {5.2.10}\leavevmode {\color {Chapter }CordaroWagnerCode}}{67}{subsection.5.2.10}
\contentsline {subsection}{\numberline {5.2.11}\leavevmode {\color {Chapter }FerreroDesignCode}}{67}{subsection.5.2.11}
\contentsline {subsection}{\numberline {5.2.12}\leavevmode {\color {Chapter }RandomLinearCode}}{68}{subsection.5.2.12}
\contentsline {subsection}{\numberline {5.2.13}\leavevmode {\color {Chapter }OptimalityCode}}{69}{subsection.5.2.13}
\contentsline {subsection}{\numberline {5.2.14}\leavevmode {\color {Chapter }BestKnownLinearCode}}{69}{subsection.5.2.14}
\contentsline {section}{\numberline {5.3}\leavevmode {\color {Chapter } Gabidulin Codes }}{71}{section.5.3}
\contentsline {subsection}{\numberline {5.3.1}\leavevmode {\color {Chapter }GabidulinCode}}{71}{subsection.5.3.1}
\contentsline {subsection}{\numberline {5.3.2}\leavevmode {\color {Chapter }EnlargedGabidulinCode}}{71}{subsection.5.3.2}
\contentsline {subsection}{\numberline {5.3.3}\leavevmode {\color {Chapter }DavydovCode}}{71}{subsection.5.3.3}
\contentsline {subsection}{\numberline {5.3.4}\leavevmode {\color {Chapter }TombakCode}}{71}{subsection.5.3.4}
\contentsline {subsection}{\numberline {5.3.5}\leavevmode {\color {Chapter }EnlargedTombakCode}}{71}{subsection.5.3.5}
\contentsline {section}{\numberline {5.4}\leavevmode {\color {Chapter } Golay Codes }}{72}{section.5.4}
\contentsline {subsection}{\numberline {5.4.1}\leavevmode {\color {Chapter }BinaryGolayCode}}{72}{subsection.5.4.1}
\contentsline {subsection}{\numberline {5.4.2}\leavevmode {\color {Chapter }ExtendedBinaryGolayCode}}{72}{subsection.5.4.2}
\contentsline {subsection}{\numberline {5.4.3}\leavevmode {\color {Chapter }TernaryGolayCode}}{73}{subsection.5.4.3}
\contentsline {subsection}{\numberline {5.4.4}\leavevmode {\color {Chapter }ExtendedTernaryGolayCode}}{73}{subsection.5.4.4}
\contentsline {section}{\numberline {5.5}\leavevmode {\color {Chapter } Generating Cyclic Codes }}{73}{section.5.5}
\contentsline {subsection}{\numberline {5.5.1}\leavevmode {\color {Chapter }GeneratorPolCode}}{74}{subsection.5.5.1}
\contentsline {subsection}{\numberline {5.5.2}\leavevmode {\color {Chapter }CheckPolCode}}{75}{subsection.5.5.2}
\contentsline {subsection}{\numberline {5.5.3}\leavevmode {\color {Chapter }RootsCode}}{75}{subsection.5.5.3}
\contentsline {subsection}{\numberline {5.5.4}\leavevmode {\color {Chapter }BCHCode}}{76}{subsection.5.5.4}
\contentsline {subsection}{\numberline {5.5.5}\leavevmode {\color {Chapter }ReedSolomonCode}}{77}{subsection.5.5.5}
\contentsline {subsection}{\numberline {5.5.6}\leavevmode {\color {Chapter }QRCode}}{77}{subsection.5.5.6}
\contentsline {subsection}{\numberline {5.5.7}\leavevmode {\color {Chapter }QQRCodeNC}}{78}{subsection.5.5.7}
\contentsline {subsection}{\numberline {5.5.8}\leavevmode {\color {Chapter }QQRCode}}{78}{subsection.5.5.8}
\contentsline {subsection}{\numberline {5.5.9}\leavevmode {\color {Chapter }FireCode}}{78}{subsection.5.5.9}
\contentsline {subsection}{\numberline {5.5.10}\leavevmode {\color {Chapter }WholeSpaceCode}}{79}{subsection.5.5.10}
\contentsline {subsection}{\numberline {5.5.11}\leavevmode {\color {Chapter }NullCode}}{79}{subsection.5.5.11}
\contentsline {subsection}{\numberline {5.5.12}\leavevmode {\color {Chapter }RepetitionCode}}{79}{subsection.5.5.12}
\contentsline {subsection}{\numberline {5.5.13}\leavevmode {\color {Chapter }CyclicCodes}}{80}{subsection.5.5.13}
\contentsline {subsection}{\numberline {5.5.14}\leavevmode {\color {Chapter }NrCyclicCodes}}{80}{subsection.5.5.14}
\contentsline {section}{\numberline {5.6}\leavevmode {\color {Chapter } Evaluation Codes }}{81}{section.5.6}
\contentsline {subsection}{\numberline {5.6.1}\leavevmode {\color {Chapter }EvaluationCode}}{81}{subsection.5.6.1}
\contentsline {subsection}{\numberline {5.6.2}\leavevmode {\color {Chapter }GeneralizedReedSolomonCode}}{81}{subsection.5.6.2}
\contentsline {subsection}{\numberline {5.6.3}\leavevmode {\color {Chapter }GeneralizedReedMullerCode}}{82}{subsection.5.6.3}
\contentsline {subsection}{\numberline {5.6.4}\leavevmode {\color {Chapter }ToricPoints}}{83}{subsection.5.6.4}
\contentsline {subsection}{\numberline {5.6.5}\leavevmode {\color {Chapter }ToricCode}}{83}{subsection.5.6.5}
\contentsline {section}{\numberline {5.7}\leavevmode {\color {Chapter } Algebraic geometric codes }}{83}{section.5.7}
\contentsline {subsection}{\numberline {5.7.1}\leavevmode {\color {Chapter }AffineCurve}}{83}{subsection.5.7.1}
\contentsline {subsection}{\numberline {5.7.2}\leavevmode {\color {Chapter }AffinePointsOnCurve}}{84}{subsection.5.7.2}
\contentsline {subsection}{\numberline {5.7.3}\leavevmode {\color {Chapter }GenusCurve}}{85}{subsection.5.7.3}
\contentsline {subsection}{\numberline {5.7.4}\leavevmode {\color {Chapter }GOrbitPoint }}{85}{subsection.5.7.4}
\contentsline {subsection}{\numberline {5.7.5}\leavevmode {\color {Chapter }DivisorOnAffineCurve}}{86}{subsection.5.7.5}
\contentsline {subsection}{\numberline {5.7.6}\leavevmode {\color {Chapter }DivisorAddition }}{87}{subsection.5.7.6}
\contentsline {subsection}{\numberline {5.7.7}\leavevmode {\color {Chapter }DivisorDegree }}{87}{subsection.5.7.7}
\contentsline {subsection}{\numberline {5.7.8}\leavevmode {\color {Chapter }DivisorNegate }}{87}{subsection.5.7.8}
\contentsline {subsection}{\numberline {5.7.9}\leavevmode {\color {Chapter }DivisorIsZero }}{87}{subsection.5.7.9}
\contentsline {subsection}{\numberline {5.7.10}\leavevmode {\color {Chapter }DivisorsEqual }}{88}{subsection.5.7.10}
\contentsline {subsection}{\numberline {5.7.11}\leavevmode {\color {Chapter }DivisorGCD }}{88}{subsection.5.7.11}
\contentsline {subsection}{\numberline {5.7.12}\leavevmode {\color {Chapter }DivisorLCM }}{88}{subsection.5.7.12}
\contentsline {subsection}{\numberline {5.7.13}\leavevmode {\color {Chapter }RiemannRochSpaceBasisFunctionP1 }}{89}{subsection.5.7.13}
\contentsline {subsection}{\numberline {5.7.14}\leavevmode {\color {Chapter }DivisorOfRationalFunctionP1 }}{90}{subsection.5.7.14}
\contentsline {subsection}{\numberline {5.7.15}\leavevmode {\color {Chapter }RiemannRochSpaceBasisP1 }}{90}{subsection.5.7.15}
\contentsline {subsection}{\numberline {5.7.16}\leavevmode {\color {Chapter }MoebiusTransformation }}{91}{subsection.5.7.16}
\contentsline {subsection}{\numberline {5.7.17}\leavevmode {\color {Chapter }ActionMoebiusTransformationOnFunction }}{92}{subsection.5.7.17}
\contentsline {subsection}{\numberline {5.7.18}\leavevmode {\color {Chapter }ActionMoebiusTransformationOnDivisorP1 }}{92}{subsection.5.7.18}
\contentsline {subsection}{\numberline {5.7.19}\leavevmode {\color {Chapter }IsActionMoebiusTransformationOnDivisorDefinedP1 }}{92}{subsection.5.7.19}
\contentsline {subsection}{\numberline {5.7.20}\leavevmode {\color {Chapter }DivisorAutomorphismGroupP1 }}{93}{subsection.5.7.20}
\contentsline {subsection}{\numberline {5.7.21}\leavevmode {\color {Chapter }MatrixRepresentationOnRiemannRochSpaceP1 }}{93}{subsection.5.7.21}
\contentsline {subsection}{\numberline {5.7.22}\leavevmode {\color {Chapter }GoppaCodeClassical}}{94}{subsection.5.7.22}
\contentsline {subsection}{\numberline {5.7.23}\leavevmode {\color {Chapter }EvaluationBivariateCode}}{95}{subsection.5.7.23}
\contentsline {subsection}{\numberline {5.7.24}\leavevmode {\color {Chapter }EvaluationBivariateCodeNC}}{95}{subsection.5.7.24}
\contentsline {subsection}{\numberline {5.7.25}\leavevmode {\color {Chapter }OnePointAGCode}}{96}{subsection.5.7.25}
\contentsline {chapter}{\numberline {6}\leavevmode {\color {Chapter }Manipulating Codes}}{98}{chapter.6}
\contentsline {section}{\numberline {6.1}\leavevmode {\color {Chapter } Functions that Generate a New Code from a Given Code }}{98}{section.6.1}
\contentsline {subsection}{\numberline {6.1.1}\leavevmode {\color {Chapter }ExtendedCode}}{98}{subsection.6.1.1}
\contentsline {subsection}{\numberline {6.1.2}\leavevmode {\color {Chapter }PuncturedCode}}{99}{subsection.6.1.2}
\contentsline {subsection}{\numberline {6.1.3}\leavevmode {\color {Chapter }EvenWeightSubcode}}{99}{subsection.6.1.3}
\contentsline {subsection}{\numberline {6.1.4}\leavevmode {\color {Chapter }PermutedCode}}{100}{subsection.6.1.4}
\contentsline {subsection}{\numberline {6.1.5}\leavevmode {\color {Chapter }ExpurgatedCode}}{100}{subsection.6.1.5}
\contentsline {subsection}{\numberline {6.1.6}\leavevmode {\color {Chapter }AugmentedCode}}{101}{subsection.6.1.6}
\contentsline {subsection}{\numberline {6.1.7}\leavevmode {\color {Chapter }RemovedElementsCode}}{101}{subsection.6.1.7}
\contentsline {subsection}{\numberline {6.1.8}\leavevmode {\color {Chapter }AddedElementsCode}}{102}{subsection.6.1.8}
\contentsline {subsection}{\numberline {6.1.9}\leavevmode {\color {Chapter }ShortenedCode}}{102}{subsection.6.1.9}
\contentsline {subsection}{\numberline {6.1.10}\leavevmode {\color {Chapter }LengthenedCode}}{103}{subsection.6.1.10}
\contentsline {subsection}{\numberline {6.1.11}\leavevmode {\color {Chapter }ResidueCode}}{104}{subsection.6.1.11}
\contentsline {subsection}{\numberline {6.1.12}\leavevmode {\color {Chapter }ConstructionBCode}}{104}{subsection.6.1.12}
\contentsline {subsection}{\numberline {6.1.13}\leavevmode {\color {Chapter }DualCode}}{104}{subsection.6.1.13}
\contentsline {subsection}{\numberline {6.1.14}\leavevmode {\color {Chapter }ConversionFieldCode}}{105}{subsection.6.1.14}
\contentsline {subsection}{\numberline {6.1.15}\leavevmode {\color {Chapter }TraceCode}}{105}{subsection.6.1.15}
\contentsline {subsection}{\numberline {6.1.16}\leavevmode {\color {Chapter }CosetCode}}{106}{subsection.6.1.16}
\contentsline {subsection}{\numberline {6.1.17}\leavevmode {\color {Chapter }ConstantWeightSubcode}}{106}{subsection.6.1.17}
\contentsline {subsection}{\numberline {6.1.18}\leavevmode {\color {Chapter }StandardFormCode}}{107}{subsection.6.1.18}
\contentsline {subsection}{\numberline {6.1.19}\leavevmode {\color {Chapter }PiecewiseConstantCode}}{107}{subsection.6.1.19}
\contentsline {section}{\numberline {6.2}\leavevmode {\color {Chapter } Functions that Generate a New Code from Two Given Codes }}{108}{section.6.2}
\contentsline {subsection}{\numberline {6.2.1}\leavevmode {\color {Chapter }DirectSumCode}}{108}{subsection.6.2.1}
\contentsline {subsection}{\numberline {6.2.2}\leavevmode {\color {Chapter }UUVCode}}{108}{subsection.6.2.2}
\contentsline {subsection}{\numberline {6.2.3}\leavevmode {\color {Chapter }DirectProductCode}}{109}{subsection.6.2.3}
\contentsline {subsection}{\numberline {6.2.4}\leavevmode {\color {Chapter }IntersectionCode}}{109}{subsection.6.2.4}
\contentsline {subsection}{\numberline {6.2.5}\leavevmode {\color {Chapter }UnionCode}}{110}{subsection.6.2.5}
\contentsline {subsection}{\numberline {6.2.6}\leavevmode {\color {Chapter }ExtendedDirectSumCode}}{110}{subsection.6.2.6}
\contentsline {subsection}{\numberline {6.2.7}\leavevmode {\color {Chapter }AmalgamatedDirectSumCode}}{111}{subsection.6.2.7}
\contentsline {subsection}{\numberline {6.2.8}\leavevmode {\color {Chapter }BlockwiseDirectSumCode}}{111}{subsection.6.2.8}
\contentsline {chapter}{\numberline {7}\leavevmode {\color {Chapter } Bounds on codes, special matrices and miscellaneous functions }}{113}{chapter.7}
\contentsline {section}{\numberline {7.1}\leavevmode {\color {Chapter } Distance bounds on codes }}{113}{section.7.1}
\contentsline {subsection}{\numberline {7.1.1}\leavevmode {\color {Chapter }UpperBoundSingleton}}{114}{subsection.7.1.1}
\contentsline {subsection}{\numberline {7.1.2}\leavevmode {\color {Chapter }UpperBoundHamming}}{114}{subsection.7.1.2}
\contentsline {subsection}{\numberline {7.1.3}\leavevmode {\color {Chapter }UpperBoundJohnson}}{114}{subsection.7.1.3}
\contentsline {subsection}{\numberline {7.1.4}\leavevmode {\color {Chapter }UpperBoundPlotkin}}{115}{subsection.7.1.4}
\contentsline {subsection}{\numberline {7.1.5}\leavevmode {\color {Chapter }UpperBoundElias}}{115}{subsection.7.1.5}
\contentsline {subsection}{\numberline {7.1.6}\leavevmode {\color {Chapter }UpperBoundGriesmer}}{116}{subsection.7.1.6}
\contentsline {subsection}{\numberline {7.1.7}\leavevmode {\color {Chapter }IsGriesmerCode}}{116}{subsection.7.1.7}
\contentsline {subsection}{\numberline {7.1.8}\leavevmode {\color {Chapter }UpperBound}}{116}{subsection.7.1.8}
\contentsline {subsection}{\numberline {7.1.9}\leavevmode {\color {Chapter }LowerBoundMinimumDistance}}{117}{subsection.7.1.9}
\contentsline {subsection}{\numberline {7.1.10}\leavevmode {\color {Chapter }LowerBoundGilbertVarshamov}}{117}{subsection.7.1.10}
\contentsline {subsection}{\numberline {7.1.11}\leavevmode {\color {Chapter }LowerBoundSpherePacking}}{117}{subsection.7.1.11}
\contentsline {subsection}{\numberline {7.1.12}\leavevmode {\color {Chapter }UpperBoundMinimumDistance}}{118}{subsection.7.1.12}
\contentsline {subsection}{\numberline {7.1.13}\leavevmode {\color {Chapter }BoundsMinimumDistance}}{118}{subsection.7.1.13}
\contentsline {section}{\numberline {7.2}\leavevmode {\color {Chapter } Covering radius bounds on codes }}{119}{section.7.2}
\contentsline {subsection}{\numberline {7.2.1}\leavevmode {\color {Chapter }BoundsCoveringRadius}}{119}{subsection.7.2.1}
\contentsline {subsection}{\numberline {7.2.2}\leavevmode {\color {Chapter }IncreaseCoveringRadiusLowerBound}}{119}{subsection.7.2.2}
\contentsline {subsection}{\numberline {7.2.3}\leavevmode {\color {Chapter }ExhaustiveSearchCoveringRadius}}{120}{subsection.7.2.3}
\contentsline {subsection}{\numberline {7.2.4}\leavevmode {\color {Chapter }GeneralLowerBoundCoveringRadius}}{121}{subsection.7.2.4}
\contentsline {subsection}{\numberline {7.2.5}\leavevmode {\color {Chapter }GeneralUpperBoundCoveringRadius}}{121}{subsection.7.2.5}
\contentsline {subsection}{\numberline {7.2.6}\leavevmode {\color {Chapter }LowerBoundCoveringRadiusSphereCovering}}{122}{subsection.7.2.6}
\contentsline {subsection}{\numberline {7.2.7}\leavevmode {\color {Chapter }LowerBoundCoveringRadiusVanWee1}}{122}{subsection.7.2.7}
\contentsline {subsection}{\numberline {7.2.8}\leavevmode {\color {Chapter }LowerBoundCoveringRadiusVanWee2}}{123}{subsection.7.2.8}
\contentsline {subsection}{\numberline {7.2.9}\leavevmode {\color {Chapter }LowerBoundCoveringRadiusCountingExcess}}{123}{subsection.7.2.9}
\contentsline {subsection}{\numberline {7.2.10}\leavevmode {\color {Chapter }LowerBoundCoveringRadiusEmbedded1}}{124}{subsection.7.2.10}
\contentsline {subsection}{\numberline {7.2.11}\leavevmode {\color {Chapter }LowerBoundCoveringRadiusEmbedded2}}{124}{subsection.7.2.11}
\contentsline {subsection}{\numberline {7.2.12}\leavevmode {\color {Chapter }LowerBoundCoveringRadiusInduction}}{125}{subsection.7.2.12}
\contentsline {subsection}{\numberline {7.2.13}\leavevmode {\color {Chapter }UpperBoundCoveringRadiusRedundancy}}{125}{subsection.7.2.13}
\contentsline {subsection}{\numberline {7.2.14}\leavevmode {\color {Chapter }UpperBoundCoveringRadiusDelsarte}}{126}{subsection.7.2.14}
\contentsline {subsection}{\numberline {7.2.15}\leavevmode {\color {Chapter }UpperBoundCoveringRadiusStrength}}{126}{subsection.7.2.15}
\contentsline {subsection}{\numberline {7.2.16}\leavevmode {\color {Chapter }UpperBoundCoveringRadiusGriesmerLike}}{126}{subsection.7.2.16}
\contentsline {subsection}{\numberline {7.2.17}\leavevmode {\color {Chapter }UpperBoundCoveringRadiusCyclicCode}}{127}{subsection.7.2.17}
\contentsline {section}{\numberline {7.3}\leavevmode {\color {Chapter } Special matrices in \textsf {GUAVA} }}{127}{section.7.3}
\contentsline {subsection}{\numberline {7.3.1}\leavevmode {\color {Chapter }KrawtchoukMat}}{128}{subsection.7.3.1}
\contentsline {subsection}{\numberline {7.3.2}\leavevmode {\color {Chapter }GrayMat}}{128}{subsection.7.3.2}
\contentsline {subsection}{\numberline {7.3.3}\leavevmode {\color {Chapter }SylvesterMat}}{128}{subsection.7.3.3}
\contentsline {subsection}{\numberline {7.3.4}\leavevmode {\color {Chapter }HadamardMat}}{129}{subsection.7.3.4}
\contentsline {subsection}{\numberline {7.3.5}\leavevmode {\color {Chapter }VandermondeMat}}{129}{subsection.7.3.5}
\contentsline {subsection}{\numberline {7.3.6}\leavevmode {\color {Chapter }PutStandardForm}}{130}{subsection.7.3.6}
\contentsline {subsection}{\numberline {7.3.7}\leavevmode {\color {Chapter }IsInStandardForm}}{131}{subsection.7.3.7}
\contentsline {subsection}{\numberline {7.3.8}\leavevmode {\color {Chapter }PermutedCols}}{131}{subsection.7.3.8}
\contentsline {subsection}{\numberline {7.3.9}\leavevmode {\color {Chapter }VerticalConversionFieldMat}}{131}{subsection.7.3.9}
\contentsline {subsection}{\numberline {7.3.10}\leavevmode {\color {Chapter }HorizontalConversionFieldMat}}{132}{subsection.7.3.10}
\contentsline {subsection}{\numberline {7.3.11}\leavevmode {\color {Chapter }MOLS}}{132}{subsection.7.3.11}
\contentsline {subsection}{\numberline {7.3.12}\leavevmode {\color {Chapter }IsLatinSquare}}{133}{subsection.7.3.12}
\contentsline {subsection}{\numberline {7.3.13}\leavevmode {\color {Chapter }AreMOLS}}{133}{subsection.7.3.13}
\contentsline {section}{\numberline {7.4}\leavevmode {\color {Chapter } Some functions related to the norm of a code }}{134}{section.7.4}
\contentsline {subsection}{\numberline {7.4.1}\leavevmode {\color {Chapter }CoordinateNorm}}{134}{subsection.7.4.1}
\contentsline {subsection}{\numberline {7.4.2}\leavevmode {\color {Chapter }CodeNorm}}{134}{subsection.7.4.2}
\contentsline {subsection}{\numberline {7.4.3}\leavevmode {\color {Chapter }IsCoordinateAcceptable}}{134}{subsection.7.4.3}
\contentsline {subsection}{\numberline {7.4.4}\leavevmode {\color {Chapter }GeneralizedCodeNorm}}{135}{subsection.7.4.4}
\contentsline {subsection}{\numberline {7.4.5}\leavevmode {\color {Chapter }IsNormalCode}}{135}{subsection.7.4.5}
\contentsline {section}{\numberline {7.5}\leavevmode {\color {Chapter } Miscellaneous functions }}{135}{section.7.5}
\contentsline {subsection}{\numberline {7.5.1}\leavevmode {\color {Chapter }CodeWeightEnumerator}}{135}{subsection.7.5.1}
\contentsline {subsection}{\numberline {7.5.2}\leavevmode {\color {Chapter }CodeDistanceEnumerator}}{136}{subsection.7.5.2}
\contentsline {subsection}{\numberline {7.5.3}\leavevmode {\color {Chapter }CodeMacWilliamsTransform}}{136}{subsection.7.5.3}
\contentsline {subsection}{\numberline {7.5.4}\leavevmode {\color {Chapter }CodeDensity}}{136}{subsection.7.5.4}
\contentsline {subsection}{\numberline {7.5.5}\leavevmode {\color {Chapter }SphereContent}}{137}{subsection.7.5.5}
\contentsline {subsection}{\numberline {7.5.6}\leavevmode {\color {Chapter }Krawtchouk}}{137}{subsection.7.5.6}
\contentsline {subsection}{\numberline {7.5.7}\leavevmode {\color {Chapter }PrimitiveUnityRoot}}{137}{subsection.7.5.7}
\contentsline {subsection}{\numberline {7.5.8}\leavevmode {\color {Chapter }PrimitivePolynomialsNr}}{138}{subsection.7.5.8}
\contentsline {subsection}{\numberline {7.5.9}\leavevmode {\color {Chapter }IrreduciblePolynomialsNr}}{138}{subsection.7.5.9}
\contentsline {subsection}{\numberline {7.5.10}\leavevmode {\color {Chapter }MatrixRepresentationOfElement}}{138}{subsection.7.5.10}
\contentsline {subsection}{\numberline {7.5.11}\leavevmode {\color {Chapter }ReciprocalPolynomial}}{139}{subsection.7.5.11}
\contentsline {subsection}{\numberline {7.5.12}\leavevmode {\color {Chapter }CyclotomicCosets}}{139}{subsection.7.5.12}
\contentsline {subsection}{\numberline {7.5.13}\leavevmode {\color {Chapter }WeightHistogram}}{140}{subsection.7.5.13}
\contentsline {subsection}{\numberline {7.5.14}\leavevmode {\color {Chapter }MultiplicityInList}}{140}{subsection.7.5.14}
\contentsline {subsection}{\numberline {7.5.15}\leavevmode {\color {Chapter }MostCommonInList}}{140}{subsection.7.5.15}
\contentsline {subsection}{\numberline {7.5.16}\leavevmode {\color {Chapter }RotateList}}{141}{subsection.7.5.16}
\contentsline {subsection}{\numberline {7.5.17}\leavevmode {\color {Chapter }CirculantMatrix}}{141}{subsection.7.5.17}
\contentsline {section}{\numberline {7.6}\leavevmode {\color {Chapter } Miscellaneous polynomial functions }}{141}{section.7.6}
\contentsline {subsection}{\numberline {7.6.1}\leavevmode {\color {Chapter }MatrixTransformationOnMultivariatePolynomial }}{141}{subsection.7.6.1}
\contentsline {subsection}{\numberline {7.6.2}\leavevmode {\color {Chapter }DegreeMultivariatePolynomial}}{141}{subsection.7.6.2}
\contentsline {subsection}{\numberline {7.6.3}\leavevmode {\color {Chapter }DegreesMultivariatePolynomial}}{142}{subsection.7.6.3}
\contentsline {subsection}{\numberline {7.6.4}\leavevmode {\color {Chapter }CoefficientMultivariatePolynomial}}{142}{subsection.7.6.4}
\contentsline {subsection}{\numberline {7.6.5}\leavevmode {\color {Chapter }SolveLinearSystem}}{143}{subsection.7.6.5}
\contentsline {subsection}{\numberline {7.6.6}\leavevmode {\color {Chapter }GuavaVersion}}{143}{subsection.7.6.6}
\contentsline {subsection}{\numberline {7.6.7}\leavevmode {\color {Chapter }CoefficientToPolynomial}}{143}{subsection.7.6.7}
\contentsline {subsection}{\numberline {7.6.8}\leavevmode {\color {Chapter }CoefficientToPolynomial}}{144}{subsection.7.6.8}
\contentsline {subsection}{\numberline {7.6.9}\leavevmode {\color {Chapter }DegreesMonomialTerm}}{144}{subsection.7.6.9}
\contentsline {subsection}{\numberline {7.6.10}\leavevmode {\color {Chapter }DivisorsMultivariatePolynomial}}{145}{subsection.7.6.10}
