Communications Toolbox

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

• .

1. Each entry A_k is either one or zero.

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

• .

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.

Note    If poly2 is a binary row vector, then gfrepcov assumes that it is already in Format 1 above and returns it unaltered.

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
  

See Also
gfpretty

gfrank

gfroots