Macaulay2
»
Documentation
Packages
»
CodingTheory
::
Index
next | previous | forward | backward | up |
index
|
toc
CodingTheory : Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
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