# gfminpol

Find minimal polynomial of Galois field element

## Syntax

```pol = gfminpol(k,m) pol = gfminpol(k,m,p) pol = gfminpol(k,prim_poly,p) ```

## Description

Note

This function performs computations in GF(pm), where p is prime. To work in GF(2m), use the `minpol` function with Galois arrays. For details, see Minimal Polynomials.

`pol = gfminpol(k,m)` produces a minimal polynomial for each entry in `k`. `k` must be either a scalar or a column vector. Each entry in `k` represents an element of GF(2m) in exponential format. That is, `k` represents alpha^`k`, where alpha is a primitive element in GF(2m). The ith row of `pol` represents the minimal polynomial of `k`(i). The coefficients of the minimal polynomial are in the base field GF(2) and listed in order of ascending exponents.

`pol = gfminpol(k,m,p)` finds the minimal polynomial of Ak over GF(`p`), where `p` is a prime number, `m` is an integer greater than 1, and A is a root of the default primitive polynomial for GF(`p^m`). The format of the output is as follows:

• If `k` is a nonnegative integer, `pol` is a row vector that gives the coefficients of the minimal polynomial in order of ascending powers.

• If `k` is a vector of length len all of whose entries are nonnegative integers, `pol` is a matrix having len rows; the rth row of `pol` gives the coefficients of the minimal polynomial of Ak(r) in order of ascending powers.

`pol = gfminpol(k,prim_poly,p)` is the same as the first syntax listed, except that A is a root of the primitive polynomial for GF(`p`m) specified by `prim_poly`. `prim_poly` is a polynomial character vector or a row vector that gives the coefficients of the degree-m primitive polynomial in order of ascending powers.

## Examples

The syntax `gfminpol(k,m,p)` is used in the sample code in Characterization of Polynomials.

## Version History

Introduced before R2006a