Cyclic codes over ${\mathbb{Z}}_4+u{\mathbb{Z}}_4$

Abstract

In this paper, we have studied cyclic codes over the ring $R={\mathbb{Z}}_4+u{\mathbb{Z}}_4$, $u^2=0$. We have considered cyclic codes of odd lengths. A sufficient condition for a cyclic code over $R$ to be a ${\mathbb{Z}}_4$-free module is presented. We have provided the general form of the generators of a cyclic code over $R$ and determined a formula for the ranks of such codes. In this paper we have mainly focused on principally generated cyclic codes of odd length over $R$. We have determined a necessary condition and a sufficient condition for cyclic codes of odd lengths over $R$ to be $R$-free.

arXiv admin note: text overlap with arXiv:1412.3751

Cited by in corpus (1)

• Characterization of the skew cyclic codes over Fp+vFp