Constructions of several families of MDS codes and NMDS codes
Yanan Yin, Haode Yan · Advances in Mathematics of Communications · 2025
Linear codes achieving or nearly achieving the Singleton bound have many nice applications in data storage, combinatorial design, secret sharing, and so on. In this paper, we present several classes of MDS codes and NMDS codes, and the parameters of these codes are determined. In addition, by applying a result proposed by Tang and Ding (IEEE Trans. Inform. Theory, 67 (1), 244-254, 2021), we prove that some of these NMDS codes support $ t $-designs, where $ t = 2, 3 $. The parameters of these $ t $-designs are also derived.