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
- Loading GUAVA
- Codewords
- Codeword
- IsCodeword
- Comparisons of Codewords
- Operations for Codewords
- VectorCodeword
- PolyCodeword
- TreatAsVector
- TreatAsPoly
- NullWord
- DistanceCodeword
- Support
- WeightCodeword
- Codes
- IsCode
- IsLinearCode
- IsCyclicCode
- Comparisons of Codes
- Operations for Codes
- Basic Functions for Codes
- Domain Functions for Codes
- Printing and Saving Codes
- GeneratorMat
- CheckMat
- GeneratorPol
- CheckPol
- RootsOfCode
- WordLength
- Redundancy
- MinimumDistance
- WeightDistribution
- InnerDistribution
- OuterDistribution
- DistancesDistribution
- IsPerfectCode
- IsMDSCode
- IsSelfDualCode
- IsSelfOrthogonalCode
- IsEquivalent
- CodeIsomorphism
- AutomorphismGroup
- Decode
- Syndrome
- SyndromeTable
- StandardArray
- Display
- CodewordNr
- Generating Unrestricted Codes
- ElementsCode
- HadamardCode
- ConferenceCode
- MOLSCode
- RandomCode
- NordstromRobinsonCode
- GreedyCode
- LexiCode
- Generating Linear Codes
- GeneratorMatCode
- CheckMatCode
- HammingCode
- ReedMullerCode
- ExtendedBinaryGolayCode
- ExtendedTernaryGolayCode
- AlternantCode
- GoppaCode
- GeneralizedSrivastavaCode
- SrivastavaCode
- CordaroWagnerCode
- RandomLinearCode
- BestKnownLinearCode
- Generating Cyclic Codes
- GeneratorPolCode
- CheckPolCode
- BinaryGolayCode
- TernaryGolayCode
- RootsCode
- BCHCode
- ReedSolomonCode
- QRCode
- FireCode
- WholeSpaceCode
- NullCode
- RepetitionCode
- CyclicCodes
- Manipulating Codes
- ExtendedCode
- PuncturedCode
- EvenWeightSubcode
- PermutedCode
- ExpurgatedCode
- AugmentedCode
- RemovedElementsCode
- AddedElementsCode
- ShortenedCode
- LengthenedCode
- ResidueCode
- ConstructionBCode
- DualCode
- ConversionFieldCode
- CosetCode
- ConstantWeightSubcode
- StandardFormCode
- DirectSumCode
- UUVCode
- DirectProductCode
- IntersectionCode
- UnionCode
- Code Records
- Bounds on codes
- UpperBoundSingleton
- UpperBoundHamming
- UpperBoundJohnson
- UpperBoundPlotkin
- UpperBoundElias
- UpperBoundGriesmer
- UpperBound
- LowerBoundMinimumDistance
- UpperBoundMinimumDistance
- BoundsMinimumDistance
- Special matrices in GUAVA
- KrawtchoukMat
- GrayMat
- SylvesterMat
- HadamardMat
- MOLS
- PutStandardForm
- IsInStandardForm
- PermutedCols
- VerticalConversionFieldMat
- HorizontalConversionFieldMat
- IsLatinSquare
- AreMOLS
- Miscellaneous functions
- SphereContent
- Krawtchouk
- PrimitiveUnityRoot
- ReciprocalPolynomial
- CyclotomicCosets
- WeightHistogram
- Extensions to GUAVA
- Some functions for the covering radius
- CoveringRadius
- BoundsCoveringRadius
- SetCoveringRadius
- IncreaseCoveringRadiusLowerBound
- ExhaustiveSearchCoveringRadius
- GeneralLowerBoundCoveringRadius
- GeneralUpperBoundCoveringRadius
- LowerBoundCoveringRadiusSphereCovering
- LowerBoundCoveringRadiusVanWee1
- LowerBoundCoveringRadiusVanWee2
- LowerBoundCoveringRadiusCountingExcess
- LowerBoundCoveringRadiusEmbedded1
- LowerBoundCoveringRadiusEmbedded2
- LowerBoundCoveringRadiusInduction
- UpperBoundCoveringRadiusRedundancy
- UpperBoundCoveringRadiusDelsarte
- UpperBoundCoveringRadiusStrength
- UpperBoundCoveringRadiusGriesmerLike
- UpperBoundCoveringRadiusCyclicCode
- New code constructions
- ExtendedDirectSumCode
- AmalgatedDirectSumCode
- BlockwiseDirectSumCode
- PiecewiseConstantCode
- Gabidulin codes
- Some functions related to the norm of a code
- CoordinateNorm
- CodeNorm
- IsCoordinateAcceptable
- GeneralizedCodeNorm
- IsNormalCode
- DecreaseMinimumDistanceLowerBound
- New miscellaneous functions
- CodeWeightEnumerator
- CodeDistanceEnumerator
- CodeMacWilliamsTransform
- IsSelfComplementaryCode
- IsAffineCode
- IsAlmostAffineCode
- IsGriesmerCode
- CodeDensity
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GAP 3.4.4
April 1997