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

05/15/2023

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by   Vidya Sagar, et al.

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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.