Minimal and Optimal binary codes obtained using $C_D$-construction over the non-unital ring $I$
Information Theory
2023-09-20 v1 math.IT
Abstract
In this article, we construct linear codes over the commutative non-unital ring of size four. We obtain their Lee-weight distributions and study their binary Gray images. Under certain mild conditions, these classes of binary codes are minimal and self-orthogonal. All codes in this article are few-weight codes. Besides, an infinite class of these binary codes consists of distance optimal codes with respect to the Griesmer bound.
Cite
@article{arxiv.2305.08781,
title = {Minimal and Optimal binary codes obtained using $C_D$-construction over the non-unital ring $I$},
author = {Vidya Sagar and Ritumoni Sarma},
journal= {arXiv preprint arXiv:2305.08781},
year = {2023}
}
Comments
16 pages. arXiv admin note: substantial text overlap with arXiv:2304.06758, 2211.15747