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Minimal and Optimal binary codes obtained using $C_D$-construction over the non-unital ring $I$ (2305.08781v1)
Published 15 May 2023 in cs.IT and math.IT
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.