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Application of optimal p-ary linear codes to alphabet-optimal locally repairable codes

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Abstract

Linear codes have widespread applications in data storage systems. There are two major contributions in this paper. We first propose infinite families of optimal or distance-optimal linear codes over \({\mathbb F}_p\) constructed from projective spaces. Moreover, a necessary and sufficient condition for such linear codes to be Griesmer codes is presented. Secondly, as an application in data storage systems, we investigate the locality of the linear codes constructed. Furthermore, we show that these linear codes are alphabet-optimal locally repairable codes with locality 2.

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Authors and Affiliations

  1. School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore, 637371, Singapore

    Gaojun Luo & San Ling

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  1. Gaojun Luo
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  2. San Ling
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Correspondence to Gaojun Luo.

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Communicated by G. Ge.

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This work was supported by NTU Research Grant 04INS000047C230GRT01.

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Luo, G., Ling, S. Application of optimal p-ary linear codes to alphabet-optimal locally repairable codes. Des. Codes Cryptogr. 90, 1271–1287 (2022). https://doi.org/10.1007/s10623-022-01040-4

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  • DOI: https://doi.org/10.1007/s10623-022-01040-4

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