CodingTheory : Index
-
alphabet -- elements of the base ring of a code
-
alphabet(LinearCode) -- elements of the base ring of a code
-
AmbientModule -- the ambient module of a code
-
ambientSpace -- recovers the ambient module of a code
-
ambientSpace(LinearCode) -- recovers the ambient module of a code
-
BaseField -- the field of a code
-
bitflipDecode -- an experimental implementation of a message passing decoder
-
bitflipDecode(Matrix,Vector,ZZ) -- an experimental implementation of a message passing decoder
-
cartesianCode -- Cartesian code
-
cartesianCode(Ring,List,List) -- Cartesian code
-
cartesianCode(Ring,List,Matrix) -- Cartesian code
-
cartesianCode(Ring,List,ZZ) -- Cartesian code
-
chooseStrat -- Estimate the optimal strategy to compute the minimum weight of a linear code.
-
chooseStrat(LinearCode) -- Estimate the optimal strategy to compute the minimum weight of a linear code.
-
Code -- a code as image
-
codewords -- codewords of the code
-
codewords(LinearCode) -- codewords of the code
-
CodingTheory -- tools for Coding Theory
-
cyclicCode -- cyclic codes
-
cyclicCode(GaloisField,RingElement,ZZ) -- cyclic codes
-
cyclicCode(GaloisField,ZZ,ZZ) -- cyclic codes
-
cyclicMatrix -- cyclic matrix
-
cyclicMatrix(GaloisField,List) -- cyclic matrix
-
cyclicMatrix(List) -- cyclic matrix
-
dim(LinearCode) -- dimension of a linear code
-
dualCode -- dual of a code
-
dualCode(LinearCode) -- dual of a code
-
enumerateVectors -- a particular way to enumerate vectors over a finite field
-
enumerateVectors(Ring,List) -- a particular way to enumerate vectors over a finite field
-
EvaluationCode -- class of evaluation codes
-
evaluationCode -- functions to construct evaluation codes over Galois fields
-
evaluationCode(Ring,List,List) -- functions to construct evaluation codes over Galois fields
-
evaluationCode(Ring,List,Matrix) -- functions to construct evaluation codes over Galois fields
-
evCodeGraph -- Reed–Muller-type code over a graph
-
evCodeGraph(Ring,Matrix,List) -- Reed–Muller-type code over a graph
-
ExponentsMatrix -- specifies the matrix of exponents
-
field -- the field of a code
-
field(LinearCode) -- the field of a code
-
footPrint -- generalized footprint function of an ideal
-
footPrint(ZZ,ZZ,Ideal) -- generalized footprint function of an ideal
-
GeneratorMatrix -- gives the generator matrix of a linear code
-
Generators -- list of generators of a code
-
generatorToParityCheck -- parity check matrix of a linear code
-
generatorToParityCheck(Matrix) -- parity check matrix of a linear code
-
genericCode -- ambient space of a code
-
genericCode(LinearCode) -- ambient space of a code
-
genMinDisIdeal -- generalized minimum distance function of an ideal
-
genMinDisIdeal(ZZ,ZZ,Ideal) -- generalized minimum distance function of an ideal
-
getLRCencodingPolynomial -- encoding polynomial for an LRC code
-
getLRCencodingPolynomial(ZZ,ZZ,List,RingElement) -- encoding polynomial for an LRC code
-
hammingCode -- generates a Hamming code
-
hammingCode(ZZ,ZZ) -- generates a Hamming code
-
hyp -- hyp function of an ideal
-
hyp(ZZ,ZZ,Ideal) -- hyp function of an ideal
-
informationRate -- information rate of a code
-
informationRate(LinearCode) -- information rate of a code
-
length(LinearCode) -- returns the length of a linear code
-
LinearCode -- class of linear codes
-
linearCode -- functions to construct linear codes over Galois fields
-
LinearCode == LinearCode -- determines if two linear codes are equal
-
linearCode(...,ParityCheck=>...) -- functions to construct linear codes over Galois fields
-
linearCode(GaloisField,List) -- functions to construct linear codes over Galois fields
-
linearCode(GaloisField,ZZ,List) -- functions to construct linear codes over Galois fields
-
linearCode(Matrix) -- functions to construct linear codes over Galois fields
-
linearCode(Module) -- functions to construct linear codes over Galois fields
-
linearCode(Module,List) -- functions to construct linear codes over Galois fields
-
linearCode(ZZ,ZZ,ZZ,List) -- functions to construct linear codes over Galois fields
-
locallyRecoverableCode -- constructs a locally recoverable code (LRC)
-
locallyRecoverableCode(List,List,RingElement) -- constructs a locally recoverable code (LRC)
-
messages -- set of messages to be encoded by a code
-
messages(LinearCode) -- set of messages to be encoded by a code
-
minimumWeight -- computes the minimum weight of a linear code
-
minimumWeight(...,Strat=>...) -- Specify the algorithm used to perform a minimum weight computation.
-
minimumWeight(LinearCode) -- computes the minimum weight of a linear code
-
orderCode -- computes an order code for a given weight
-
orderCode(Ideal,List,List,ZZ) -- computes an order code for a given weight
-
orderCode(Ideal,List,ZZ) -- computes an order code for a given weight
-
orderCode(Ring,List,List,ZZ) -- computes an order code for a given weight
-
ParityCheck -- an optional input for the linearCode constructor
-
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
-
parityCheckToGenerator(Matrix) -- generator matrix given a parity check matrix
-
PolynomialSet -- a set of polynomials for an evaluation code
-
quasiCyclicCode -- constructs a quasi-cyclic code
-
quasiCyclicCode(GaloisField,List) -- constructs a quasi-cyclic code
-
quasiCyclicCode(List) -- constructs a quasi-cyclic code
-
randLDPC -- low density parity check matrix
-
randLDPC(ZZ,ZZ,RR,ZZ) -- low density parity check matrix
-
randNoRepeats -- list of random integers from a specified range with no repetitions
-
randNoRepeats(ZZ,ZZ) -- list of random integers from a specified range with no repetitions
-
randomCode -- constructs a random linear code over a finite field
-
randomCode(GaloisField,ZZ,ZZ) -- constructs a random linear code over a finite field
-
randomCode(QuotientRing,ZZ,ZZ) -- constructs a random linear code over a finite field
-
reducedMatrix -- reduced matrix
-
reducedMatrix(Matrix) -- reduced matrix
-
reedMullerCode -- constructs the Reed-Muller code
-
reedMullerCode(ZZ,ZZ,ZZ) -- constructs the Reed-Muller code
-
reedSolomonCode -- constructs the Reed-Solomon code
-
reedSolomonCode(Ring,List,ZZ) -- constructs the Reed-Solomon code
-
repetitionCode -- repetition code
-
repetitionCode(GaloisField,ZZ) -- repetition code
-
ring(LinearCode) -- the ring of a code
-
Sets -- sets of a Cartesian code
-
shorten -- shortens a code
-
shorten(LinearCode,List) -- shortens a code
-
shorten(LinearCode,ZZ) -- shortens a code
-
shortestPath -- shorthest path in a digraph
-
shortestPath(Digraph,Thing,List) -- shorthest path in a digraph
-
size(LinearCode) -- gives the number of codewords in a linear code
-
Strat -- Specify the algorithm used to perform a minimum weight computation.
-
syndromeDecode -- syndrome decoding on a code
-
syndromeDecode(LinearCode,Matrix,ZZ) -- syndrome decoding on a code
-
tannerGraph -- outputs the tanner graph associated with the given parity check matrix
-
tannerGraph(Matrix) -- outputs the tanner graph associated with the given parity check matrix
-
toricCode -- a toric code construction
-
toricCode(Ring,Matrix) -- a toric code construction
-
toString(LinearCode) -- string with the vectors of a generator matrix of a code
-
universeCode -- linear code $\mathtt{F}^\mathtt{n}$
-
universeCode(GaloisField,ZZ) -- linear code $\mathtt{F}^\mathtt{n}$
-
VanishingIdeal -- vanishing ideal of an evaluation code
-
vasconcelosDegree -- Vasconcelos function of an ideal
-
vasconcelosDegree(ZZ,ZZ,Ideal) -- Vasconcelos function of an ideal
-
vectorSpace -- vector space of a code
-
vectorSpace(LinearCode) -- vector space of a code
-
vNumber -- the v-number of a graded ideal
-
vNumber(Ideal) -- the v-number of a graded ideal
-
weight -- Hamming weight of a list
-
weight(BasicList) -- Hamming weight of a list
-
zeroCode -- zero code
-
zeroCode(GaloisField,ZZ) -- zero code
-
zeroSumCode -- linear code in which the entries of each codeword add up zero
-
zeroSumCode(GaloisField,ZZ) -- linear code in which the entries of each codeword add up zero