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

Jian Gao; Xiangrui Meng; Fang-Wei Fu

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arXiv · 2203.12149

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

Jian Gao·Xiangrui Meng·Fang-Wei Fu

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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 $\mathbb{Z}_4$.

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Jian Gao, Xiangrui Meng, Fang-Wei Fu. 2022-03-23. On generalized quasi-cyclic codes over $\mathbb{Z}_4$. https://arxiv.org/abs/2203.12149

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