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Title: Optimal RS-like LRC codes of arbitrary length
Authors: Rajput C.
Bhaintwal, Maheshanand
Published in: Applicable Algebra in Engineering, Communications and Computing
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+1r+1, where r is the locality of the code. They also proposed a construction with this condition lifted to n≠1mod(r+1)n≠1mod(r+1). In a recent paper, Kolosov et al. (Optimal LRC codes for all lenghts n≤qn≤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≤qn≤q. Further, we show that the codes constructed by the proposed construction are optimal LRC codes for their parameters.
Citation: Applicable Algebra in Engineering, Communications and Computing (2020), 31(3): 271-289
Issue Date: 2020
Keywords: LRC codes · RS-like LRC codes · Shortened codes · Optimal LRC codes
Author Scopus IDs: 57216530687
Author Affiliations: Rajput, C., Indian Institute of Technology Roorkee, Roorkee, 247667, India
Bhaintwal, M., Indian Institute of Technology Roorkee, Roorkee, 247667, India
Appears in Collections:Journal Publications [MA]

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