gfrepcov

Convert one binary polynomial representation to another

Syntax

polystandard = gfrepcov(poly2)


Description

Two logical ways to represent polynomials over GF(2) are listed below.

1. [A_0 A_1 A_2 ... A_(m-1)] represents the polynomial

   $$\text{A\_}0+\text{A\_1}x+\text{A\_2}{x}^2+\cdots +\text{A\_(m-1)}{x}^{m-1}$$

   Each entry A_k is either one or zero.

2. [A_0 A_1 A_2 ... A_(m-1)] represents the polynomial

   $$x^{\text{A\_0}}+x^{\text{A\_1}}+x^{\text{A\_2}}+\cdots +x^{\text{A\_(m-1)}}$$

   Each entry A_k is a nonnegative integer. All entries must be distinct.

Format 1 is the standard form used by the Galois field functions in this toolbox, but there are some cases in which format 2 is more convenient.

polystandard = gfrepcov(poly2) converts from the second format to the first, for polynomials of degree at least 2. poly2 and polystandard are row vectors. The entries of poly2 are distinct integers, and at least one entry must exceed 1. Each entry of polystandard is either 0 or 1.

Examples

The command below converts the representation format of the polynomial 1 + x² + x⁵.

polystandard = gfrepcov([0 2 5])

polystandard =

     1     0     1     0     0     1

Version History

Introduced before R2006a