Cyclic codes over $Z_2 + uZ_2 + u^2Z_2 + . . . + u^{k−1}Z_2$

Abstract

In this paper, we study the structure of cyclic codes of an arbitrary length n over the ring $Z_2 + uZ_2 + u^2Z_2 + . . . + u^{k−1}Z_2$, where $u^k = 0$. Also we study the rank for these codes, and we find their minimal spanning sets. This study is a generalization and extension of the work in reference [1].