1-generator two-dimensional quasi-cyclic codes over Z_4[u]/(u^2-1)

Arazgol  Ghajari; Kazem   Khashyarmanesh; Zohreh  Rajabi

Arazgol Ghajari
Kazem Khashyarmanesh
Zohreh Rajabi

Keywords: Two-dimensional cyclic codes, Two-dimensional quasi-cyclic codes, Two-dimensional generalized quasi-cyclic codes

Abstract

In this paper, we obtain generating set of polynomials of two-dimensional cyclic codes over the ring R=Z₄[u]/(u²-1), where u²=1. Moreover, we find generator polynomials for two-dimensional quasi-cyclic 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.

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