Communications Toolbox

gfplus

Add elements of a Galois field of characteristic two

Syntax

k = gfplus(a,b,fvec,ivec);

Description

k = gfplus(a,b,fvec,ivec) adds a and b in GF(2^m), using the exponential format to represent inputs and outputs. If a and b are matrices, then they must have the same dimensions, and gfplus adds them element-by-element. See Representing Elements of Galois Fields for an explanation of the exponential format.

fvec and ivec are vectors of length 2^m. The entries in both are integers between 0 and 2^m-1. fvec contains the same information as the field parameter as used by gfadd, except that fvec has been condensed into a vector. To compute fvec and ivec, define m and then use the commands below.

fvec = gftuple([-1 : 2^m-2]',m) * 2.^[0 : m-1]';
ivec(fvec + 1) = 0 : 2^m - 1;

Alternatively, define a primitive polynomial vector pol and then use the commands below. See gfprimfd for information about defining pol.

fvec = gftuple([-1 : 2^m-2]',pol) * 2.^[0 : m-1]';
ivec(fvec + 1) = 0 : 2^m - 1;

Examples

This example adds two matrices, each of which contains random nonzero elements of GF(2⁵).

m = 5;
a = randint(3,6,2^m-1,1234); % Create a 3-by-6 matrix in GF(2^5).
b = randint(3,6,2^m-1);
fvec = gftuple([-1 : 2^m - 2]',m)*2.^[0 : m-1]';
ivec(fvec + 1) = 0 : 2^m - 1;
aplusb = gfplus(a,b,fvec,ivec) % Add.

aplusb =

    22    25     4    23     9    29
     9    30    24    23  -Inf    19
    15    17    10    12    25    30

See Also
gfadd, gfsub

gfmul

gfpretty