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Syntax

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

Description

Note

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.

Examples

Arithmetic in Galois Fields contains examples. Also, the code below shows that

A 2 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 =

Version History

Introduced before R2006a

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