2022/10/11 by Ziling Heng, Xinran Wang, Heng, Ziling +1 · 2 citations
Computer Science · Engineering · #Cellular Automata and Applications #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2210.05194
openalex publication_date 2022/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In ``Infinite families of near MDS codes holding t-designs, IEEE Trans. Inform. Theory, 2020, 66(9), pp. 5419-5428'', Ding and Tang made a breakthrough in constructing the first two infinite families of NMDS codes holding 2-designs or 3-designs. Up to now, there are only a few known infinite families of NMDS codes holding t-designs in the literature. The objective of this paper is to construct new infinite families of NMDS codes holding t-designs. We determine the weight enumerators of the NMDS codes and prove that the NMDS codes hold 2-designs or 3-designs. Compared with known t-designs from NMDS codes, ours have different parameters. Besides, several infinite families of optimal locally recoverable codes are also derived via the NMDS codes.