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arXiv · 2203.05301

Double Constacyclic Codes over Two Finite Commutative Chain Rings

Yun Fan·Hualu Liu
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Abstract

Many kinds of codes which possess two cycle structures over two special finite commutative chain rings, such as ${\Bbb Z}_2{\Bbb Z}_4$-additive cyclic codes and quasi-cyclic codes of fractional index etc., were proved asymptotically good. In this paper we extend the study in two directions: we consider any two finite commutative chain rings with a surjective homomorphism from one to the other, and consider double constacyclic structures. We construct an extensive kind of double constacyclic codes over two finite commutative chain rings. And, developing a probabilistic method suitable for quasi-cyclic codes over fields, we prove that the double constacyclic codes over two finite commutative chain rings are asymptotically good.

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Yun Fan, Hualu Liu. 2022-03-10. Double Constacyclic Codes over Two Finite Commutative Chain Rings. https://arxiv.org/abs/2203.05301

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