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

Vidya Sagar; Ritumoni Sarma

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arXiv · 2305.08781

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

Vidya Sagar·Ritumoni Sarma

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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.

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Vidya Sagar, Ritumoni Sarma. 2023-05-15. Minimal and Optimal binary codes obtained using $C_D$-construction over the non-unital ring $I$. https://arxiv.org/abs/2305.08781

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