Communications Toolbox

gfminpol

Find minimal polynomial of a Galois field element

Syntax

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

Description

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

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, then 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, then 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 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.

See Also

gfprimdf, gfcosets, gfroots, Galois Fields of Odd Characteristic

gflineq

gfmul

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