Communications Toolbox

Testing for Equality

To compare corresponding elements of two Galois arrays that have the same size, use the operators == and ~=. The result is a logical array, each element of which indicates the truth or falsity of the corresponding elementwise comparison. If you use the same operators to compare a scalar with a Galois array, then MATLAB compares the scalar with each element of the array, producing a logical array of the same size.

m = 5; r1 = gf([1:3],m); r2 = 1 ./ r1;
lg1 = (r1 .* r2 == [1 1 1]) % Does each element equal one?
lg2 = (r1 .* r2 == 1) % Same as above, using scalar expansion
lg3 = (r1 ~= r2) % Does each element differ from its inverse?

The output is below.

lg1 =

     1     1     1


lg2 =

     1     1     1


lg3 =

     0     1     1

Comparison of isequal and ==

To compare entire arrays and obtain a logical scalar result rather than a logical array, you can use the built-in isequal function. Note, however, that isequal uses strict rules for its comparison, and returns a value of 0 (false) if you compare

• A Galois array with an ordinary MATLAB array, even if the values of the underlying array elements match

• A scalar with a nonscalar array, even if all elements in the array match the scalar

The example below illustrates this difference between == and isequal.

m = 5; r1 = gf([1:3],m); r2 = 1 ./ r1;
lg4 = isequal(r1 .* r2, [1 1 1]); % False
lg5 = isequal(r1 .* r2, gf(1,m)); % False
lg6 = isequal(r1 .* r2, gf([1 1 1],m)); % True

Logical Operations in Galois Fields

Testing for Nonzero Values

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