Two-dimensional constacyclic codes over finite chain rings

Vaishali Singh; Sucheta Dutt; Ridhima Thakral

Two-dimensional constacyclic codes over finite chain rings

信息论 2026-07-10 v1

作者: Vaishali Singh , Sucheta Dutt , Ridhima Thakral

摘要

The main focus of this paper is on the algebraic structure of two-dimensional $(\lambda,\mu)$ -constacyclic codes of length $\ell\mathrm{m}$ over finite chain rings with residue field $\mathbb{F}_q$ , where $q \equiv 1 \pmod{r\mathrm{m}}$ and $r$ denotes the multiplicative order of $\bar{\mu}$ . In this paper, the structure of two-dimensional $(\lambda,\mu)$ -constacyclic codes is obtained. Our approach relies on analysing primitive idempotents within the finite chain ring to determine the generators of these codes. We also find the condition under which two-dimensional constacyclic codes are maximum Hamming distance with respect to rank (MHDR) over finite chain rings.

引用

@article{arxiv.2607.09117,
  title  = {Two-dimensional constacyclic codes over finite chain rings},
  author = {Vaishali Singh and Sucheta Dutt and Ridhima Thakral},
  journal= {arXiv preprint arXiv:2607.09117},
  year   = {2026}
}