Documentation

# Galois Fields

Manipulate elements of finite fields

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

## Functions

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 `convmtx` Convolution matrix of Galois field vector `cosets` Produce cyclotomic cosets for Galois field `dftmtx` Discrete Fourier transform matrix in Galois field `fft` Discrete Fourier transform `filter (gf)` 1-D digital filter over Galois field `gf` Create Galois field array `gftable` Generate file to accelerate Galois field computations `ifft` Inverse discrete Fourier transform `isprimitive` True for primitive polynomial for Galois field `log` Logarithm in Galois field `minpol` Find minimal polynomial of Galois field element `mldivide` Matrix left division \ of Galois arrays `primpoly` Find primitive polynomials for Galois field
 `gfadd` Add polynomials over Galois field `gfconv` Multiply polynomials over Galois field `gfcosets` Produce cyclotomic cosets for Galois field `gfdeconv` Divide polynomials over Galois field `gfdiv` Divide elements of Galois field `gffilter` Filter data using polynomials over prime Galois field `gflineq` Find particular solution of Ax = b over prime Galois field `gfminpol` Find minimal polynomial of Galois field element `gfmul` Multiply elements of Galois field `gfpretty` Polynomial in traditional format `gfprimck` Check whether polynomial over Galois field is primitive `gfprimdf` Provide default primitive polynomials for Galois field `gfprimfd` Find primitive polynomials for Galois field `gfrank` Compute rank of matrix over Galois field `gfrepcov` Convert one binary polynomial representation to another `gfroots` Find roots of polynomial over prime Galois field `gfsub` Subtract polynomials over Galois field `gftrunc` Minimize length of polynomial representation `gftuple` Simplify or convert Galois field element formatting

## Topics

Working with Galois Fields

This example illustrates how to work with Galois fields.