2022/11/28 by Sagar, Vidya, Sarma, Ritumoni
#05E45 #94B05 #94B60 #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2211.15747
In this manuscript, we work over the non-chain ring R = \mathbbF2[u]/⟨ u3 - u⟩ . Let m∈ ℕ and let L, M, N ⊆ [m]:=\1, 2, …, m\. For X⊆ [m], define ΔX:=\v ∈ \mathbbF2m : \textnormalSupp(v)⊆ X\ and D:= (1+u2)D1 + u2D2 + (u+u2)D3, an ordered finite multiset consisting of elements from Rm, where D1∈ \ΔL, ΔLc\, D2∈ \ΔM, ΔMc\, D3∈ \ΔN, ΔNc\. The linear code CD over R defined by \(v⋅ d)d∈ D : v ∈ Rm \ is studied for each D. Further, we also consider simplicial complexes with two maximal elements in the above work. We study their binary Gray images and the binary subfield-like codes corresponding to a certain \mathbbF2-functional of R. Sufficient conditions for these binary linear codes to be minimal and self-orthogonal are obtained in each case. Besides, we produce an infinite family of optimal codes with respect to the Griesmer bound. Most of the codes obtained in this manuscript are few-weight codes.