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Applicable Algebra in Engineering, Communication and Computing

Erschienen in:

15.04.2020 | Original Paper

Optimal RS-like LRC codes of arbitrary length

verfasst von: Charul Rajput, Maheshanand Bhaintwal

Erschienen in: Applicable Algebra in Engineering, Communication and Computing | Ausgabe 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.

Vorheriger Artikel A trigonometric approach for Dickson polynomials over fields of characteristic two

Nächster Artikel Hamming distance of repeated-root constacyclic codes of length over

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Titel: Optimal RS-like LRC codes of arbitrary length
verfasst von: Charul Rajput
Maheshanand Bhaintwal
Publikationsdatum: 15.04.2020
Verlag: Springer Berlin Heidelberg
Erschienen in: Applicable Algebra in Engineering, Communication and Computing / Ausgabe 3-4/2020
Print ISSN: 0938-1279
Elektronische ISSN: 1432-0622
DOI: https://doi.org/10.1007/s00200-020-00430-2

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