Convert one binary polynomial representation to another
polystandard = gfrepcov(poly2)
Two logical ways to represent polynomials over GF(2) are listed below.
[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.
[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.
Note:
If |
The command below converts the representation format of the polynomial 1 + x^{2} + x^{5}.
polystandard = gfrepcov([0 2 5])
polystandard = 1 0 1 0 0 1