Documentation

### This is machine translation

Mouseover text to see original. Click the button below to return to the English version of the page.

Note: This page has been translated by MathWorks. Click here to see
To view all translated materials including this page, select Country from the country navigator on the bottom of this page.

# Galois Fields

Manipulate elements of finite fields

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

## Functions

expand all

 `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.