1-generator two-dimensional quasi-cyclic codes over $\mathbb{Z}_4[u]/\langle u^2-1\rangle$

Abstract

In this paper, we obtain generating set of polynomials of two-dimensional cyclic codes over the ring R = Z4[u]/ u 2 −1 , where u 2 = 1. Moreover, we find generator polynomials for two-dimensional quasicyclic codes and two-dimensional generalized quasi-cyclic codes over R and specify a lower bound on minimum distance of free 1-generator two-dimensional quasi-cyclic codes and two-dimensional generalized quasi-cyclic codes over R.