Galois Field Computations

convmtxConvolution matrix of Galois field vector
cosetsProduce cyclotomic cosets for a Galois field
dftmtxDiscrete Fourier transform matrix in a Galois field
fftDiscrete Fourier transform
filter (gf)One-dimensional digital filter over a Galois field
gfCreate Galois field array
gftableGenerate file to accelerate Galois field computations
ifftInverse discrete Fourier transform
isprimitiveTrue for primitive polynomial for a Galois field
logLogarithm in a Galois field
minpolFind minimal polynomial of a Galois field element
mldivideMatrix left division \ of Galois arrays
primpolyFind primitive polynomials for a Galois field

Some additional MATLAB functions that the Communications Toolbox enhances to process elements of Galois fields are below.

+ -Addition and subtraction of Galois arrays
* / \Matrix multiplication and division of Galois arrays
.* ./ .\Elementwise multiplication and division of Galois arrays
^Matrix exponentiation of Galois array
.^Elementwise exponentiation of Galois array
' .'Transpose of Galois array
==, ~=Relational operators for Galois arrays
allTrue if all elements of a Galois vector are nonzero
anyTrue if any element of a Galois vector is nonzero
convConvolution of Galois vectors
deconvDeconvolution and polynomial division
detDeterminant of square Galois matrix
diagDiagonal Galois matrices and diagonals of a Galois matrix
invInverse of Galois matrix
isemptyTrue for empty Galois arrays
lengthLength of Galois vector
luLower-upper triangular factorization of Galois array
polyvalEvaluate polynomial in Galois field
rankRank of a Galois array
reshapeReshape Galois array
rootsFind polynomial roots across a Galois field
sizeSize of Galois array
trilExtract lower triangular part of Galois array
triuExtract upper triangular part of Galois array


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