Two classes of NMDS codes from Roth-Lempel codes
Zhonghao Liang, Qunying Liao
TL;DR
This paper introduces two new classes of NMDS codes derived from Roth-Lempel codes, generalizing recent constructions and fully characterizing their weight distributions for improved error correction.
Contribution
It presents novel NMDS code classes based on Roth-Lempel codes, extending previous work and providing complete weight distribution analysis.
Findings
Two classes of NMDS codes constructed from Roth-Lempel codes
Complete determination of their weight distributions
Generalization of Han's and Zheng's recent constructions
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.
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Taxonomy
TopicsDNA and Biological Computing · Coding theory and cryptography · Mechanisms of cancer metastasis