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Near MDS Codes with Dimension 4 and Their Application in Locally Recoverable Codes

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Arithmetic of Finite Fields (WAIFI 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13638))

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Abstract

In this paper, several infinite families of near MDS codes with dimension four are constructed with special matrixes and oval polynomials. The weight enumerators of them are explicitly determined. As an application, the duals of these near NMDS codes are proved to be both distance-optimal and dimension-optimal locally recoverable codes.

This work was supported by Natural Science Foundation of China under Grant 11901049, in part by the Young Talent Fund of University Association for Science and Technology in Shaanxi, China, under Grant 20200505 and in part by the Fundamental Research Funds for the Central Universities, CHD, under Grant 300102122202.

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Authors and Affiliations

  1. School of Science, Chang’an University, Xi’an, 710064, China

    Ziling Heng & Xiaoru Li

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  1. Ziling Heng
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  2. Xiaoru Li
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Correspondence to Xiaoru Li .

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Editors and Affiliations

  1. Department of Mathematics, University of Paris VIII, Paris, France

    Sihem Mesnager

  2. School of Mathematics, Southwest Jiaotong University, Chengdu, China

    Zhengchun Zhou

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Heng, Z., Li, X. (2023). Near MDS Codes with Dimension 4 and Their Application in Locally Recoverable Codes. In: Mesnager, S., Zhou, Z. (eds) Arithmetic of Finite Fields. WAIFI 2022. Lecture Notes in Computer Science, vol 13638. Springer, Cham. https://doi.org/10.1007/978-3-031-22944-2_8

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  • DOI: https://doi.org/10.1007/978-3-031-22944-2_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-22943-5

  • Online ISBN: 978-3-031-22944-2

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