log - Logarithm in Galois field

Syntax

Description

y = log(x) computes the logarithm of each element in the Galois array x. y is an integer array that solves the equation A.^y = x, where A is the primitive element used to represent elements in x. More explicitly, the base A of the logarithm is gf(2,x.m) or gf(2,x.m,x.prim_poly). All elements in x must be nonzero because the logarithm of zero is undefined.

Examples

The code below illustrates how the logarithm operation inverts exponentiation.

m = 4; x = gf([8 1 6; 3 5 7; 4 9 2],m);
y = log(x);
primel = gf(2,m); % Primitive element in the field
z = primel .^ y; % This is now the same as x.
ck = isequal(x,z)

The output is

ck =

     1

The code below shows that the logarithm of 1 is 0 and that the logarithm of the base (primel) is 1.

m = 4; primel = gf(2,m);
yy = log([1, primel])

The output is

yy =

     0     1

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