Quadratic residue code

Definition
Let $$p$$ be a prime. The quadratic residue code associated with $$p$$ is the binary linear code defined as follows:


 * The underlying set is the set $$F_p$$
 * The subspace involved is the subspace generated by all translates of the set of quadratic non-residues

In other words, it is a cyclic code with generator polynomial being the generating function for the quadratic non-residues.

Particular cases

 * Golay code