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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 $I$
- 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
- Subjects :
- Computer Science - Information Theory
94B05, 16L30, 05E45
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2305.08781
- Document Type :
- Working Paper