Two classes of NMDS codes from Roth-Lempel codes

2025/06/24 by Zhonghao Liang, Liang, Zhonghao, Qunying Liao +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #DNA and Biological Computing #Coding theory and cryptography #Mechanisms of cancer metastasis

paper · pdf · doi:10.48550/arxiv.2506.19346

Abstract

Since near maximum distance separable (NMDS) codes have good algebraic properties and excellent error-correcting capabilities, they have been widely used in various fields such as communication systems, data storage, quantum codes, and so on. In this paper, basing on the generator matrix of Roth-Lempel codes, we present two classes of NMDS codes which generalize Han's and Zheng's constructions in 2023 and 2025, respectively. And we also completely determine their weight distributions.

Citations

• Some constructions of non-generalized Reed-Solomon MDS Codes
• Several new infinite families of NMDS codes with arbitrary dimensions supporting t-designs
• New families of non-Reed-Solomon MDS codes
• More MDS codes of non-Reed-Solomon type
• Near-MDS Codes from Maximal Arcs in PG(2,q)
• On the subset sum problem over finite fields
• A family of linear codes that are either non-GRS MDS codes or NMDS codes

Cited by

• The extended code for a class of generalized Roth-Lempel codes and their properties

Related

• New MDS codes of non-GRS type and NMDS codes
• On the equivalence of NMDS codes
• Several new infinite families of NMDS codes with arbitrary dimensions supporting t-designs
• The extended code for a class of generalized Roth-Lempel codes and their properties
• Constructions of near MDS codes which are optimal locally recoverable codes