On the cyclic order distribution and partitioning of linear cyclic codes (Q2042188)

In this paper, the authors present a method to directly compute the number of codewords of \(C\) with cyclic order \(i\), for \(1\leq i\leq n\) and \(i|n\), and consequently the number of cyclic equivalence classes of \(C\) (practically, it is 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. Moreover, the authors prove a theorem to directly obtain the leaders of the cyclic equivalence classes of a linear cyclic code \(C\) (no other constraints except the size of the finite field and the block length of the code must be coprimes). Finally, they present a criterion to construct maximal cyclic order codes.