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arXiv · 2103.11665

New constructions of MDS self-dual and self-orthogonal codes via GRS codes

Ziteng Huang·Weijun Fang·Fang-Wei Fu
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Abstract

Recently, the construction of new MDS Euclidean self-dual codes has been widely investigated. In this paper, for square q, we utilize generalized Reed-Solomon (GRS) codes and their extended codes to provide four generic families of q-ary MDS Euclidean self-dual codes. In particular, for large square q, our constructions take up a proportion of generally more than 34% in all the possible lengths of q-ary MDS Euclidean self-dual codes, which is larger than the previous results. Moreover, two new families of MDS Euclidean self-orthogonal codes and two new families of MDS Euclidean almost self-dual codes are given similarly.

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Ziteng Huang, Weijun Fang, Fang-Wei Fu. 2021-03-22. New constructions of MDS self-dual and self-orthogonal codes via GRS codes. https://arxiv.org/abs/2103.11665

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