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Minimal and Optimal binary codes obtained using $C_D$-construction over the non-unital ring $I$

Minimal and Optimal binary codes obtained using $C_D$-construction over the non-unital ring $I$

Authors :
Sagar, Vidya
Sarma, Ritumoni
Publication Year :
2023

Abstract

In this article, we construct linear codes over the commutative non-unital ring $I$ 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.<br />Comment: 16 pages. arXiv admin note: substantial text overlap with arXiv:2304.06758, 2211.15747

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2305.08781
Document Type :
Working Paper