Communications Toolbox

Example: Elementwise Logarithm

The code below computes the logarithm of the elements of a Galois array. The output indicates how to express each nonzero element of GF(8) as a power of the primitive element. The logarithm of the zero element of the field is undefined.

gf8_nonzero = gf([1:7],3); % Vector of nonzero elements of GF(8)
expformat = log(gf8_nonzero) % Logarithm of each element

The output is

expformat =

     0     1     3     2     6     4     5

As an example of how to interpret the output, consider the last entry in each vector in this example. You can infer that the element gf(7,3) in GF(8) can be expressed as either

• A⁵, using the last element of expformat

• A²+A+1, using the binary representation of 7 as 111. See Example: Representing Elements of GF(8) for more details.

Example: Exponentiation

Logical Operations in Galois Fields

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