Galois Fields

Manipulate elements of finite fields

Communications Toolbox™ allows you to manipulate finite fields having both even and odd orders.


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convmtxConvolution matrix of Galois field vector
cosetsProduce cyclotomic cosets for Galois field
dftmtxDiscrete Fourier transform matrix in Galois field
fftDiscrete Fourier transform
filter (gf)1-D digital filter over Galois field
gfGalois field array
gftableGenerate file to accelerate Galois field computations
ifftInverse discrete Fourier transform
isprimitiveTrue for primitive polynomial for Galois field
logLogarithm in Galois field
minpolFind minimal polynomial of Galois field element
mldivideMatrix left division \ of Galois arrays
primpolyFind primitive polynomials for Galois field
gfaddAdd polynomials over Galois field
gfconvMultiply polynomials over Galois field
gfcosetsProduce cyclotomic cosets for Galois field
gfdeconvDivide polynomials over Galois field
gfdivDivide elements of Galois field
gffilterFilter data using polynomials over prime Galois field
gflineqFind particular solution of Ax = b over prime Galois field
gfminpolFind minimal polynomial of Galois field element
gfmulMultiply elements of Galois field
gfprettyPolynomial in traditional format
gfprimckCheck whether polynomial over Galois field is primitive
gfprimdfProvide default primitive polynomials for Galois field
gfprimfdFind primitive polynomials for Galois field
gfrankCompute rank of matrix over Galois field
gfrepcovConvert one binary polynomial representation to another
gfrootsFind roots of polynomial over prime Galois field
gfsubSubtract polynomials over Galois field
gftruncMinimize length of polynomial representation
gftupleSimplify or convert Galois field element formatting


Working with Galois Fields

This example illustrates how to work with Galois fields.

Character Representation of Polynomials

You can specify polynomials as a character vector or string using a variety of syntaxes that correspond to those found in literature.

Featured Examples