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arXiv · 2308.01593

New constructions of NMDS self-dual codes

Dongchun Han·Hanbin Zhang
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Abstract

Near maximum distance separable (NMDS) codes are important in finite geometry and coding theory. Self-dual codes are closely related to combinatorics, lattice theory, and have important application in cryptography. In this paper, we construct a class of $q$-ary linear codes and prove that they are either MDS or NMDS which depends on certain zero-sum condition. In the NMDS case, we provide an effective approach to construct NMDS self-dual codes which largely extend known parameters of such codes. In particular, we proved that for square $q$, almost $q/8$ NMDS self-dual $q$-ary codes can be constructed.

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Dongchun Han, Hanbin Zhang. 2023-08-03. New constructions of NMDS self-dual codes. https://arxiv.org/abs/2308.01593

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