Factorization of cyclic codes

Abstract

A subclass of cyclic codes of composite block lengthn=n' \cdot n", withn'andn"relatively prime, is studied. It is shown how, under certain conditions, these codes may be factorized into subcodes of block lengthn'andn"and how they are related to codes of block lengthn'orn", over extension fields of the base field. The problem is, in a sense, the converse of the one considered by Burton and Weldon, [5] and some of our codes are subcodes of their product codes. The factorization property gives better insight into the structure of various codes and allows, in particular, to obtain new lower bounds on their minimum weight, hence improving in many cases on the Bose-Chaudhuri bound.