Double Constacyclic Codes over Two Finite Commutative Chain Rings

TL;DR

This paper extends the study of codes with two cycle structures over finite commutative chain rings, introducing double constacyclic codes and proving their asymptotic goodness using probabilistic methods.

Contribution

It introduces double constacyclic codes over two finite commutative chain rings and proves their asymptotic goodness, extending previous work on related code structures.

Findings

Double constacyclic codes are constructed over two finite commutative chain rings.

These codes are proven to be asymptotically good using probabilistic methods.

The study generalizes previous results on codes with two cycle structures.

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.