Quadratic residue code

From Groupprops
Revision as of 11:07, 3 April 2007 by Vipul (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

Template:Binary linear code type


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