Locally recoverable $J$-affine variety codes

Carlos Galindo; Fernando Hernando; Carlos Munuera

doi:10.1016/j.ffa.2020.101661

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arXiv · 1911.07485

Locally recoverable $J$-affine variety codes

Carlos Galindo·Fernando Hernando·Carlos Munuera

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Abstract

A locally recoverable (LRC) code is a code over a finite field $\mathbb{F}_q$ such that any erased coordinate of a codeword can be recovered from a small number of other coordinates in that codeword. We construct LRC codes correcting more than one erasure, which are subfield-subcodes of some $J$-affine variety codes. For these LRC codes, we compute localities $(r, \delta)$ that determine the minimum size of a set $\bar{R}$ of positions so that any $\delta- 1$ erasures in $\bar{R}$ can be recovered from the remaining $r$ coordinates in this set. We also show that some of these LRC codes with lengths $n\gg q$ are $(\delta-1)$-optimal.

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Carlos Galindo, Fernando Hernando, Carlos Munuera. 2019-11-18. Locally recoverable $J$-affine variety codes. https://doi.org/10.1016/j.ffa.2020.101661

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