新的无限族的近MDS码持有$t$-设计和最优的局部可恢复码

SIAM J. Discret. Math. Pub Date : 2022-10-11 DOI:10.48550/arXiv.2210.05194

Ziling Heng, Xinran Wang

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引用次数: 3

摘要

在“持有$t$-设计的无限族近MDS码”中，IEEE Trans。通知。“理论，2020,66(9)，pp. 5419-5428”，Ding和Tang在构造前两个具有$2$-设计或$3$-设计的无限族NMDS代码方面取得了突破。到目前为止，文献中已知的具有$t$-设计的无限族NMDS码很少。本文的目的是构造具有$t$-设计的新的无限族NMDS码。我们确定了NMDS码的权重枚举数，并证明了NMDS码持有$2$设计或$3$设计。与NMDS规范中已知的$t$-设计相比，我们的设计具有不同的参数。此外，还利用NMDS码导出了若干无限族的最优局部可恢复码。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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New infinite families of near MDS codes holding $t$-designs and optimal locally recoverable codes

In ``Infinite families of near MDS codes holding $t$-designs, IEEE Trans. Inform. Theory, 2020, 66(9), pp. 5419-5428'', Ding and Tang made a breakthrough in constructing the first two infinite families of NMDS codes holding $2$-designs or $3$-designs. Up to now, there are only a few known infinite families of NMDS codes holding $t$-designs in the literature. The objective of this paper is to construct new infinite families of NMDS codes holding $t$-designs. We determine the weight enumerators of the NMDS codes and prove that the NMDS codes hold $2$-designs or $3$-designs. Compared with known $t$-designs from NMDS codes, ours have different parameters. Besides, several infinite families of optimal locally recoverable codes are also derived via the NMDS codes.

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SIAM J. Discret. Math.

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