arXiv subjects

Nilay Kumar Mondal

Publications and source records attributed to Nilay Kumar Mondal.

2 recordsLinked to original sources

arXiv2026

New Quaternary codes with small Plotkin-defects from two-generator simplicial complexes

In this article, we construct infinite families of quaternary (that is, over the ring $\mathbb{Z}_4$) $\mathcal{C}_{D}$-codes, where the defining set $D$ is derived utilizing a two-generator simplicial complex, and determine their Lee weight distributions. As a result, we find three quaternary linear code families with Plotkin-defect 1 \& 2 and report at least 32 new or improved parameters having small Plotkin-defects, including 19 projective and 7 optimal parameters. We additionally report 5 quaternary linear codes with best-known parameters that are also projective. Further, we establish necessary and sufficient conditions for their Gray image to be linear, which in turn gives two infinite families of distance-optimal, one infinite family of at least almost dimension-optimal binary linear codes and five infinite families of minimal binary linear codes.

cs.IT↗

arXiv2022

A class of few-Lee weight $\mathbb{Z}_2[u]$-linear codes using simplicial complexes and minimal codes via Gray map

Recently some mixed alphabet rings are involved in constructing few-Lee weight additive codes with optimal or minimal Gray images using suitable defining sets or down-sets. Inspired by these works, we choose the mixed alphabet ring $\mathbb{Z}_2\mathbb{Z}_2[u]$ to construct a special class of linear code $C_L$ over $\mathbb{Z}_2[u]$ with $u^2=0$ by employing simplicial complexes generated by a single maximal element. We show that $C_L$ has few-Lee weights by determining the Lee weight distribution of $C_L$. Theoretically, this shows that we may employ simplicial complexes to obatin few-weight codes even in the case of mixed alphabet rings. We show that the Gray image of $C_L$ is self-orthogonal and we have an infinite family of minimal codes over $\mathbb{Z}_2$ via Gray map, which can be used to secret sharing schemes.

cs.IT↗