log
Logarithm in Galois field
Syntax
y = log(x)
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
Version History
Introduced before R2006a