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Applicable Algebra in Engineering, Communication and Computing

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15-04-2020 | Original Paper

Optimal RS-like LRC codes of arbitrary length

Authors: Charul Rajput, Maheshanand Bhaintwal

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 3-4/2020

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Abstract

RS-like locally recoverable (LRC) codes have construction based on the classical construction of Reed–Solomon (RS) codes, where codewords are obtained as evaluations of suitably chosen polynomials. These codes were introduced by Tamo and Barg (IEEE Trans Inf Theory 60(8):4661–4676, 2014) where they assumed that the length n of the code is divisible by \(r+1\), where r is the locality of the code. They also proposed a construction with this condition lifted to \(n \ne 1 \bmod (r+1)\). In a recent paper, Kolosov et al. (Optimal LRC codes for all lenghts \(n \le q\), arXiv:1802.00157, 2018) have given an explicit construction of optimal LRC codes with this lifted condition on n. In this paper we remove any such restriction on n completely, i.e., we propose constructions for q-ary RS-like LRC codes of any length \(n \le q\). Further, we show that the codes constructed by the proposed construction are optimal LRC codes for their parameters.

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Title: Optimal RS-like LRC codes of arbitrary length
Authors: Charul Rajput
Maheshanand Bhaintwal
Publication date: 15-04-2020
Publisher: Springer Berlin Heidelberg
Published in: Applicable Algebra in Engineering, Communication and Computing / Issue 3-4/2020
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI: https://doi.org/10.1007/s00200-020-00430-2

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Special Issue: “Computer Algebra and Application to Combinatorics, Coding Theory and Cryptography” ACA 2019, Montreal, Canada, July 16–20, 2019

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