Optimal linear codes with few weights from simplicial complexes

2024/07/14 by Chen, Bing, Xu, Yunge, Hu, Zhao +2 · 2 citations
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.2407.10074

Abstract

Recently, constructions of optimal linear codes from simplicial complexes have attracted much attention and some related nice works were presented. Let q be a prime power. In this paper, by using the simplicial complexes of \mathbb F_q^m with one single maximal element, we construct four families of linear codes over the ring \mathbb F_q+u\mathbb F_q (u²=0), which generalizes the results of [IEEE Trans. Inf. Theory 66(6):3657-3663, 2020]. The parameters and Lee weight distributions of these four families of codes are completely determined. Most notably, via the Gray map, we obtain several classes of optimal linear codes over \mathbb F_q, including (near) Griesmer codes and distance-optimal codes.

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• Linear codes over a mixed-alphabet ring and their Gray images with applications to projective and locally repairable codes
• New Quaternary codes with small Plotkin-defects from two-generator simplicial complexes

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