Communications Toolbox

Exponential Format

This format uses the property that every nonzero element of GF(p^m) can be expressed as A^c for some integer c between 0 and p^m-2. Higher exponents are not needed, because the theory of Galois fields implies that every nonzero element of GF(p^m) satisfies the equation x^q-1 = 1 where q = p^m.

The use of the exponential format is shown in the table below.

Element of GF(pm)	MATLAB Representation of the Element
0	-Inf
A0 = 1	0
A1	1
Aq-2 where q = pm	q-2

Although -Inf is the standard exponential representation of the zero element, all negative integers are equivalent to -Inf when used as input arguments in exponential format. This equivalence can be useful; for example, see the concise line of code at the end of the section Default Primitive Polynomials.

Note    The equivalence of all negative integers and -Inf as exponential formats means that, for example, -1 does not represent A-1, the multiplicative inverse of A. Instead, -1 represents the zero element of the field.

Representing Elements of Galois Fields

Polynomial Format