2015 IEEE Information Theory Workshop (ITW) 2015
DOI: 10.1109/itw.2015.7133128
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Cyclic linear binary locally repairable codes

Abstract: Locally repairable codes (LRCs) are a class of codes designed for the local correction of erasures. They have received considerable attention in recent years due to their applications in distributed storage. Most existing results on LRCs do not explicitly take into consideration the field size q, i.e., the size of the code alphabet. In particular, for the binary case, only a few specific results are known by Goparaju and Calderbank. Recently, however, an upper bound on the dimension k of LRCs was presented by … Show more

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Cited by 42 publications
(16 citation statements)
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“…It can be seen from the corollary 5 and its proof that d ⊥ i ≤ ir + 1 for r ≥ 2, t ≥ 2. Hence using this upper bound, the bound in (45) can be wriiten as: which is tighter than the bound given in [13]. The bound given in [13] is for information symbol availability.…”
Section: A Field-size Dependent Bound On Minimum Distance Of An (N mentioning
confidence: 93%
See 3 more Smart Citations
“…It can be seen from the corollary 5 and its proof that d ⊥ i ≤ ir + 1 for r ≥ 2, t ≥ 2. Hence using this upper bound, the bound in (45) can be wriiten as: which is tighter than the bound given in [13]. The bound given in [13] is for information symbol availability.…”
Section: A Field-size Dependent Bound On Minimum Distance Of An (N mentioning
confidence: 93%
“…Hence using this upper bound, the bound in (45) can be wriiten as: which is tighter than the bound given in [13]. The bound given in [13] is for information symbol availability. But here we consider all symbol availability.…”
Section: A Field-size Dependent Bound On Minimum Distance Of An (N mentioning
confidence: 93%
See 2 more Smart Citations
“…Among the different classes of codes used as good candidates for local recovering, cyclic codes and subfield-subcodes of cyclic codes play an important role, as the cyclic shifts of a recovery set provide again recovery sets [1,10,12,17]. In this article we continue this line of research by using the very general language of affine variety codes.…”
Section: Introductionmentioning
confidence: 99%