Difference between revisions of "Quadratic residue code"

Latest revision as of 00:05, 8 May 2008

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.

Particular cases

• Golay code