# Quadratic residue code

From Groupprops

Template:Binary linear code type

## Definition

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

- The underlying set is the set
- 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.