On the cyclic order distribution and partitioning of linear cyclic codes

Abstract

In this paper, we propose a way to partition any linear cyclic code in its cyclic equivalence classes according to the algebraic structure of the code. Such partition is useful to generate cyclically permutable codes directly from linear cyclic codes. We consider the case where the size of the finite field and the block length of the code are coprimes. Moreover, we present a criterion to construct maximal cyclic order codes.