# 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(p^{m}),
where p is prime. To work in GF(2^{m}), 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(2^{m}) in exponential format.
That is, `k`

represents alpha^`k`

,
where alpha is a primitive element in GF(2^{m}).
The *i*th 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 A^{k} 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 A^{k(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**