Note: This page has been translated by MathWorks. Please click here

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

Multiply elements of Galois field

`c = gfmul(a,b,p) `

c = gfmul(a,b,field)

This function performs computations in GF(p^{m})
where p is prime. To work in GF(2^{m}), apply
the `.*`

operator to Galois arrays. For details,
see Example: Multiplication.

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

Was this topic helpful?