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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(pm) 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.