On the number of ℤp-double cyclic codes and quasi cyclic codes

Abstract

In this paper, we study the class of & Zopf;(p)-double cyclic codes of length n = r + s. We give a closed formula for the number of & Zopf;(p) -double cyclic codes of length n = r + s, for any integers r and s that are relatively prime to p. Moreover, we give a closed formula for the number of quasi-cyclic (QC) codes of length n = 2s and index 2. We also provide formulas for the number of separable and non-separable & Zopf;(p)-double cyclic codes of length n. In order to illustrate the results, we calculate the number of some codes with different r and s. Moreover, we list optimal parameter & Zopf;(2)-double cyclic codes for specific values of r and s.