Example

The polynomial X⁷ - 1 in Z/2Z[X] is the following product of irreducible polynomials:

(X + 1) · (X³ + X + 1) · (X³ + X² + 1).

If g = X³ + X + 1, then the cyclic code generated by g is a linear (7,4)-code.

Compare this code with the code discussed in the previous section.