gfrepcov

R2026b

Convert exponent format polynomial to standard binary format polynomial

Syntax

Q = gfrepcov(P)

Description

Q = gfrepcov(P) converts exponent format polynomial to standard binary format polynomial. For more information, see Polynomial Representations.

Examples

Convert Exponent Format to Standard Binary Coefficient Format

This example shows how to convert the exponent format representation of the polynomial $1+x^2+x^5$ to the standard binary coefficient format.

polystandard = gfrepcov([0 2 5])

polystandard = 1×6

     1     0     1     0     0     1

The result [1 0 1 0 0 1] represents the polynomial $1+x^2+x^5$ in standard binary coefficient format, where each position corresponds to the coefficient for $x^0$, $x^1$, $x^2$, $x^3$, $x^4$, $x^5$ respectively.

Input Arguments

P — Exponent format polynomial

row vector of distinct nonnegative integers

Exponent format polynomial, specified as a row vector of distinct nonnegative integers where at least one entry must exceed 1.

Data Types: double

Output Arguments

Q — Standard binary coefficient format polynomial

row vector of 0s and 1s

Standard binary coefficient format polynomial, returned as a row vector of 0s and 1s.

Data Types: double

More About

Polynomial Representations

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

• Standard binary coefficients format where [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.

• Exponent format where [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.

The standard format is used by Galois field functions, but exponent format may be more convenient in some cases.

Version History

Introduced before R2006a