On generalized quasi-cyclic codes over ${\mathbb{Z}}_4$

Abstract

Based on good algebraic structures and practicabilities, generalized quasi-cyclic (GQC) codes play important role in coding theory. In this paper, we study some results on GQC codes over ${\mathbb{Z}}_4$ including the normalized generating set, the minimum generating set and the normalized generating set of their dual codes. As an application, new ${\mathbb{Z}}_4$-linear codes and good nonlinear binary codes are constructed from GQC codes over ${\mathbb{Z}}_4$.