2019
DOI: 10.1109/tit.2019.2924888
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Universal and Dynamic Locally Repairable Codes With Maximal Recoverability via Sum-Rank Codes

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Cited by 106 publications
(129 citation statements)
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“…However, they became popular when they were used for improving the performance of multishot network coding built on rank-metric codes [32]. Later, sum-rank-metric codes have also been used in distributed storage, playing a crucial role in some special constructions of partial MDS codes [27,28].…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…However, they became popular when they were used for improving the performance of multishot network coding built on rank-metric codes [32]. Later, sum-rank-metric codes have also been used in distributed storage, playing a crucial role in some special constructions of partial MDS codes [27,28].…”
Section: Introductionmentioning
confidence: 99%
“…We recall a slightly different notion of sum-rank metric code, in which the codewords are vectors with entries from an extension field F q m rather than matrices over F q . The interested reader is referred to [26,28,29,31,34] for a more detailed description of this setting. The F q -rank of a vector v = (v 1 , .…”
Section: Introductionmentioning
confidence: 99%
“…More precisely, we show that for any rate R P p0, 1q such that R ‰ 1{2, there exists an explicit MDP convolutional code with rate R and degree δ P tk, n ´ku over a finite field of size Θpn 2δ q. The idea behind our construction differs from the existing constructions and is based on the theory of skew polynomials [15], [16], which has seen important applications in other areas of coding theory such as distributed storage [17], [18].…”
Section: Introductionmentioning
confidence: 98%
“…Upper bounds on the minimum Hamming distance were proved, e.g., Singleton-type bounds [7], [17], [31], [41], and bounds related with the alphabet size [1], [5]. Optimal LRCs (with respect to these bounds), were constructed, e.g., [13], [24], [28], [34], [37], [38], [42]. In [10], [21], lower bounds on the field size of optimal LRCs were derived for δ = 2 [21], and δ 2 [10].…”
Section: Introductionmentioning
confidence: 99%
“…In [19], lower bounds on the field size requirement for MR codes were introduced. For explicit constructions of MR codes, the reader may refer to [3], [8], [15], [16], [18], [20], [28]. Notably, there are MR codes have order-optimal field size (with respect to the bound in [19]): [3] for a single global parity check (h = 1), [4], [19] for h = 2, [16] for h = 3 and δ = 2, and [8], [18] for h δ + 1 a constant, and n = Θ(r 2 ).…”
Section: Introductionmentioning
confidence: 99%