Quadratic residue code

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Template:Binary linear code type

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