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