Abstract
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.
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