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On generalized quasi-cyclic codes over $\mathbb{Z}_4$ (2203.12149v1)
Published 23 Mar 2022 in math.RA, cs.IT, and math.IT
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 $\mathbb{Z}_4$.