minpol

R2026b

Find minimal polynomial of Galois field element

Syntax

poly = minpol(A)

Description

poly = minpol(A) finds the minimal polynomial of each element in the Galois column vector, A.

Note

The output is in GF(2) even if the input is in a different Galois field.

Examples

Find Minimum Polynomial

Show that the minimal polynomial of gf(2,4) is the primitive polynomial used for the field $GF(2^m)$. This is true for any value of m, not just the value used in the example.

m = 4;
A = gf(2,m)

 
A = GF(2^4) array. Primitive polynomial = D^4+D+1 (19 decimal)
 
Array elements = 
 
   2

poly = minpol(A)

 
poly = GF(2) array. 
 
Array elements = 
 
   1   0   0   1   1

The row vector [1 0 0 1 1] represents the polynomial $D^4+D+1$.

Input Arguments

A — Galois field array

Galois field array

Galois field array, specified as a variable that MATLAB^® recognizes as a Galois field array. Use the gf to create Galois field arrays.

Data Types: Galois field array

Output Arguments

poly — Minimal polynomials

matrix

Minimal polynomials, returned as a matrix of zero-padded minimal polynomials. The output poly is an array in GF(2). The kth row of poly lists the coefficients, in order of descending powers, of the minimal polynomial of the kth element of A.

Version History

Introduced before R2006a