Quasi-cyclic codes as cyclic codes over a family of local rings

摘要

We give an algebraic structure for a large family of binary quasi-cyclic codes. We construct a family of commutative rings and a canonical Gray map such that cyclic codes over this family of rings produce quasi-cyclic codes of arbitrary index in the Hamming space via the Gray map. We use the Gray map to produce optimal linear codes that are quasi-cyclic. (C) 2016 Elsevier Inc. All rights reserved.