Documentation

This is machine translation

Mouseover text to see original. Click the button below to return to the English version of the page.

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 ```