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This is a Quantitative Study study.

October 2, 2025Open Access

Two classes of NMDS codes from Roth-Lempel codes

Key Points

The proposed NMDS codes demonstrate excellent error-correcting capabilities, enhancing existing constructions.
Two new classes of NMDS codes were derived from Roth-Lempel codes, generalizing previous works by Han and Zheng.
The research includes a complete determination of weight distributions for the new classes of NMDS codes.
These NMDS codes are applicable in communication systems and quantum coding, reflecting their practical significance.

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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Cite This Study

Liang et al. (Tue,) studied this question.

synapsesocial.com/papers/68de84bf5b556a9128e1be10 https://doi.org/https://doi.org/10.48550/arxiv.2506.19346

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