Constacyclic codes, cocycles and a u+v|u-v construction

Abstract

A connection between cohomology, cocycles and constacyclic codes is explored. It suggests an isomorphism between cyclic codes of length mn and a direct sum of m constacyclic codes of length n. The isomorphism is used (i) to study the discrete Fourier transforms and the decomposition of group ring codes; (ii) to give a u+v|u-v construction over GF(q) when q is odd. The u+v|u-v construction gives some of the best ternary cyclic codes and classes of "nearly MDS" cyclic codes of length 2q+2. The symmetry of the construction is used to give a new proof that there are no cyclic self-dual codes over GF(q), when q is odd.