65 GUAVA

GUAVA is a share library package that implements coding theory algorithms in GAP. Codes can be created and manipulated and information about codes can be calculated.

GUAVA consists of various files written in the GAP language, and an external program from J.S.~Leon for dealing with automorphism groups of codes and isomorphism testing functions. Several algorithms that need the speed are integrated in the GAP kernel. Please send your bug reports to the gap-forum (GAP-Forum@Math.RWTH-Aachen.DE).

GUAVA is written as a final project during our study of Mathematics at the Delft University of Technology, department of Pure Mathematics, and in Aachen, at Lehrstuhl D fuer Mathematik.

We would like to thank the GAP people at the RWTH Aachen for their support, A.E.~Brouwer for his advice and J.~Simonis for his supervision.

Jasper Cramwinckel,
Erik Roijackers, and
Reinald Baart.

Delft University of Technology
Faculty of Technical Mathematics and Informatics
Department of Pure Mathematics

As of version~1.3, new functions are added. These functions are also written in Delft as a final project during my study of Mathematics. For more information, see Extensions to GUAVA.

Eric Minkes.

The following sections describe the functions of the GUAVA (Version~1.3) share libary package for computing with codes. All functions described here are written entirely in the GAP language, except for the automorphism group and isomorphism testing functions, which make use of J.S.~Leon's partition backtrack programs.

GUAVA is primarily designed for the construction and analysis of codes. The functions can be divided into three subcategories:

Construction of codes:

GUAVA can construct unrestricted, linear and cyclic codes. Information about the code is stored in a record, together with operations applicable to the code.

Manipulations of codes:

Manipulation transforms one code into another, or constructs a new code from two codes. The new code can profit from the data in the record of the old code(s), so in these cases calculation time decreases.

Computations of information about codes:

GUAVA can calculate important data of codes very fast. The results are stored in the code record.

Subsections

  1. Loading GUAVA
  2. Codewords
  3. Codeword
  4. IsCodeword
  5. Comparisons of Codewords
  6. Operations for Codewords
  7. VectorCodeword
  8. PolyCodeword
  9. TreatAsVector
  10. TreatAsPoly
  11. NullWord
  12. DistanceCodeword
  13. Support
  14. WeightCodeword
  15. Codes
  16. IsCode
  17. IsLinearCode
  18. IsCyclicCode
  19. Comparisons of Codes
  20. Operations for Codes
  21. Basic Functions for Codes
  22. Domain Functions for Codes
  23. Printing and Saving Codes
  24. GeneratorMat
  25. CheckMat
  26. GeneratorPol
  27. CheckPol
  28. RootsOfCode
  29. WordLength
  30. Redundancy
  31. MinimumDistance
  32. WeightDistribution
  33. InnerDistribution
  34. OuterDistribution
  35. DistancesDistribution
  36. IsPerfectCode
  37. IsMDSCode
  38. IsSelfDualCode
  39. IsSelfOrthogonalCode
  40. IsEquivalent
  41. CodeIsomorphism
  42. AutomorphismGroup
  43. Decode
  44. Syndrome
  45. SyndromeTable
  46. StandardArray
  47. Display
  48. CodewordNr
  49. Generating Unrestricted Codes
  50. ElementsCode
  51. HadamardCode
  52. ConferenceCode
  53. MOLSCode
  54. RandomCode
  55. NordstromRobinsonCode
  56. GreedyCode
  57. LexiCode
  58. Generating Linear Codes
  59. GeneratorMatCode
  60. CheckMatCode
  61. HammingCode
  62. ReedMullerCode
  63. ExtendedBinaryGolayCode
  64. ExtendedTernaryGolayCode
  65. AlternantCode
  66. GoppaCode
  67. GeneralizedSrivastavaCode
  68. SrivastavaCode
  69. CordaroWagnerCode
  70. RandomLinearCode
  71. BestKnownLinearCode
  72. Generating Cyclic Codes
  73. GeneratorPolCode
  74. CheckPolCode
  75. BinaryGolayCode
  76. TernaryGolayCode
  77. RootsCode
  78. BCHCode
  79. ReedSolomonCode
  80. QRCode
  81. FireCode
  82. WholeSpaceCode
  83. NullCode
  84. RepetitionCode
  85. CyclicCodes
  86. Manipulating Codes
  87. ExtendedCode
  88. PuncturedCode
  89. EvenWeightSubcode
  90. PermutedCode
  91. ExpurgatedCode
  92. AugmentedCode
  93. RemovedElementsCode
  94. AddedElementsCode
  95. ShortenedCode
  96. LengthenedCode
  97. ResidueCode
  98. ConstructionBCode
  99. DualCode
  100. ConversionFieldCode
  101. CosetCode
  102. ConstantWeightSubcode
  103. StandardFormCode
  104. DirectSumCode
  105. UUVCode
  106. DirectProductCode
  107. IntersectionCode
  108. UnionCode
  109. Code Records
  110. Bounds on codes
  111. UpperBoundSingleton
  112. UpperBoundHamming
  113. UpperBoundJohnson
  114. UpperBoundPlotkin
  115. UpperBoundElias
  116. UpperBoundGriesmer
  117. UpperBound
  118. LowerBoundMinimumDistance
  119. UpperBoundMinimumDistance
  120. BoundsMinimumDistance
  121. Special matrices in GUAVA
  122. KrawtchoukMat
  123. GrayMat
  124. SylvesterMat
  125. HadamardMat
  126. MOLS
  127. PutStandardForm
  128. IsInStandardForm
  129. PermutedCols
  130. VerticalConversionFieldMat
  131. HorizontalConversionFieldMat
  132. IsLatinSquare
  133. AreMOLS
  134. Miscellaneous functions
  135. SphereContent
  136. Krawtchouk
  137. PrimitiveUnityRoot
  138. ReciprocalPolynomial
  139. CyclotomicCosets
  140. WeightHistogram
  141. Extensions to GUAVA
  142. Some functions for the covering radius
  143. CoveringRadius
  144. BoundsCoveringRadius
  145. SetCoveringRadius
  146. IncreaseCoveringRadiusLowerBound
  147. ExhaustiveSearchCoveringRadius
  148. GeneralLowerBoundCoveringRadius
  149. GeneralUpperBoundCoveringRadius
  150. LowerBoundCoveringRadiusSphereCovering
  151. LowerBoundCoveringRadiusVanWee1
  152. LowerBoundCoveringRadiusVanWee2
  153. LowerBoundCoveringRadiusCountingExcess
  154. LowerBoundCoveringRadiusEmbedded1
  155. LowerBoundCoveringRadiusEmbedded2
  156. LowerBoundCoveringRadiusInduction
  157. UpperBoundCoveringRadiusRedundancy
  158. UpperBoundCoveringRadiusDelsarte
  159. UpperBoundCoveringRadiusStrength
  160. UpperBoundCoveringRadiusGriesmerLike
  161. UpperBoundCoveringRadiusCyclicCode
  162. New code constructions
  163. ExtendedDirectSumCode
  164. AmalgatedDirectSumCode
  165. BlockwiseDirectSumCode
  166. PiecewiseConstantCode
  167. Gabidulin codes
  168. Some functions related to the norm of a code
  169. CoordinateNorm
  170. CodeNorm
  171. IsCoordinateAcceptable
  172. GeneralizedCodeNorm
  173. IsNormalCode
  174. DecreaseMinimumDistanceLowerBound
  175. New miscellaneous functions
  176. CodeWeightEnumerator
  177. CodeDistanceEnumerator
  178. CodeMacWilliamsTransform
  179. IsSelfComplementaryCode
  180. IsAffineCode
  181. IsAlmostAffineCode
  182. IsGriesmerCode
  183. CodeDensity
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GAP 3.4.4
April 1997