Multiply elements of Galois field
c = gfmul(a,b,p)
c = gfmul(a,b,field)
Note:
This function performs computations in GF(p^{m})
where p is prime. To work in GF(2^{m}), apply
the |
The gfmul
function multiplies elements of
a Galois field. (To multiply polynomials over a Galois field, use gfconv
instead.)
c = gfmul(a,b,p)
multiplies a
and b
in
GF(p
). Each entry of a
and b
is
between 0 and p
-1. p
is a prime
number. If a
and b
are matrices
of the same size, the function treats each element independently.
c = gfmul(a,b,field)
multiplies a
and b
in
GF(p^{m}), where p is a prime number and m
is a positive integer. a
and b
represent
elements of GF(p^{m}) in exponential format
relative to some primitive element of GF(p^{m}). field
is
the matrix listing all elements of GF(p^{m}),
arranged relative to the same primitive element. c
is
the exponential format of the product, relative to the same primitive
element. See Representing Elements of Galois Fields for an explanation
of these formats. If a
and b
are
matrices of the same size, the function treats each element independently.
Arithmetic in Galois Fields contains examples. Also, the code below shows that
$${A}^{2}\cdot {A}^{4}={A}^{6}$$
where A is a root of the primitive polynomial 2 + 2x + x^{2} for GF(9).
p = 3; m = 2; prim_poly = [2 2 1]; field = gftuple([-1:p^m-2]',prim_poly,p); a = gfmul(2,4,field)
The output is
a = 6