CodingTheory : Table of Contents

• CodingTheory -- tools for Coding Theory

  • EvaluationCode -- class of evaluation codes

    • evaluationCode -- functions to construct evaluation codes over Galois fields

      • evCodeGraph -- Reed–Muller-type code over a graph
      • cartesianCode -- Cartesian code

        • Sets -- sets of a Cartesian code
      • orderCode -- computes an order code for a given weight
      • reedSolomonCode -- constructs the Reed-Solomon code
      • reedMullerCode -- constructs the Reed-Muller code
      • toricCode -- a toric code construction

        • ExponentsMatrix -- specifies the matrix of exponents
    • footPrint -- generalized footprint function of an ideal
    • genMinDisIdeal -- generalized minimum distance function of an ideal
    • hyp -- hyp function of an ideal
    • vasconcelosDegree -- Vasconcelos function of an ideal
    • vNumber -- the v-number of a graded ideal
    • PolynomialSet -- a set of polynomials for an evaluation code
    • VanishingIdeal -- vanishing ideal of an evaluation code
  • LinearCode -- class of linear codes

    • ambientSpace -- recovers the ambient module of a code

      • alphabet -- elements of the base ring of a code
      • AmbientModule -- the ambient module of a code
      • BaseField -- the field of a code
      • field -- the field of a code
      • vectorSpace -- vector space of a code
    • bitflipDecode -- an experimental implementation of a message passing decoder
    • Code -- a code as image
    • codewords -- codewords of the code
    • GeneratorMatrix -- gives the generator matrix of a linear code

      • Generators -- list of generators of a code
    • informationRate -- information rate of a code
    • linearCode -- functions to construct linear codes over Galois fields

      • cyclicCode -- cyclic codes

        • cyclicMatrix -- cyclic matrix
        • quasiCyclicCode -- constructs a quasi-cyclic code
      • dualCode -- dual of a code
      • genericCode -- ambient space of a code
      • hammingCode -- generates a Hamming code
      • locallyRecoverableCode -- constructs a locally recoverable code (LRC)

        • getLRCencodingPolynomial -- encoding polynomial for an LRC code
      • ParityCheck -- an optional input for the linearCode constructor

        • generatorToParityCheck -- parity check matrix of a linear code
        • ParityCheckMatrix -- a parity check matrix of a code
        • ParityCheckRows -- rows of a parity check matrix of a code
        • parityCheckToGenerator -- generator matrix given a parity check matrix
        • randLDPC -- low density parity check matrix
        • tannerGraph -- outputs the tanner graph associated with the given parity check matrix
      • randomCode -- constructs a random linear code over a finite field
      • repetitionCode -- repetition code
      • shorten -- shortens a code
      • universeCode -- linear code $\mathtt{F}^\mathtt{n}$
      • zeroCode -- zero code
      • zeroSumCode -- linear code in which the entries of each codeword add up zero
    • messages -- set of messages to be encoded by a code
    • weight -- Hamming weight of a list

      • minimumWeight -- computes the minimum weight of a linear code

        • chooseStrat -- Estimate the optimal strategy to compute the minimum weight of a linear code.
        • Strat -- Specify the algorithm used to perform a minimum weight computation.
    • syndromeDecode -- syndrome decoding on a code
    • LinearCode == LinearCode -- determines if two linear codes are equal
  • dim(LinearCode) -- dimension of a linear code
  • length(LinearCode) -- returns the length of a linear code
  • ring(LinearCode) -- the ring of a code
  • size(LinearCode) -- gives the number of codewords in a linear code
  • toString(LinearCode) -- string with the vectors of a generator matrix of a code
  • enumerateVectors -- a particular way to enumerate vectors over a finite field
  • randNoRepeats -- list of random integers from a specified range with no repetitions
  • reducedMatrix -- reduced matrix
  • shortestPath -- shorthest path in a digraph