Linear codes invariant with respect to generalized shift operators

Abstract

The purpose of this paper is to introduce new linear codes with generalized symmetry. We extend cyclic and group codes in the following way. We introduce codes, invariant with respect to a family of generalized shift operators (GSO). In particle case when this family is a group (cyclic or Abelian), these codes are ordinary cyclic and group codes. They are invariant with respect to this group. We deal with GSO-invariant codes with fast code and encode procedures based on fast generalized Fouriertransforms. The hope is that these more general structures will lead to larger classes of useful codes “good” properties.