Communications Toolbox

Example: Multiplication

The example below multiplies individual elements in a Galois array using the .* operator. It then performs matrix multiplication using the * operator. The elementwise multiplication produces an array whose size matches that of the inputs. By contrast, the matrix multiplication produces a Galois scalar because it is the matrix product of a row vector with a column vector.

m = 5;
row1 = gf([1:2:9],m); row2 = gf([2:2:10],m);
col = row2'; % Transpose to create a column array.
ep = row1 .* row2; % Elementwise product.
mp = row1 * col; % Matrix product.

Multiplication Table for GF(8)

As another example, the code below multiplies two Galois vectors using matrix multiplication. The result is a multiplication table for GF(8).

m = 3;
els = gf([0:2^m-1]',m);
multb = els * els' % Multiply els by its own matrix transpose.

The output is below.

multb = GF(2^3) array. Primitive polynomial = D^3+D+1 (11 decimal)
 
Array elements = 
 
     0     0     0     0     0     0     0     0
     0     1     2     3     4     5     6     7
     0     2     4     6     3     1     7     5
     0     3     6     5     7     4     1     2
     0     4     3     7     6     2     5     1
     0     5     1     4     2     7     3     6
     0     6     7     1     5     3     2     4
     0     7     5     2     1     6     4     3

Example: Addition and Subtraction

Example: Division

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