2017
DOI: 10.1007/978-3-319-63931-4_4
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Locally Recoverable Codes from Algebraic Curves and Surfaces

Abstract: A locally recoverable code is a code over a finite alphabet such that the value of any single coordinate of a codeword can be recovered from the values of a small subset of other coordinates. Building on work of Barg, Tamo, and Vlȃduţ, we present several constructions of locally recoverable codes from algebraic curves and surfaces.

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Cited by 40 publications
(41 citation statements)
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“…Note that this is in fact an exact equality because of the upper bound (2). Moreover, as is easily checked, the code C as a whole meets the upper bound (4) with equality.…”
Section: A Automorphisms Of Rational Function Fieldsmentioning
confidence: 77%
“…Note that this is in fact an exact equality because of the upper bound (2). Moreover, as is easily checked, the code C as a whole meets the upper bound (4) with equality.…”
Section: A Automorphisms Of Rational Function Fieldsmentioning
confidence: 77%
“…Locally recoverable codes have been the subject of intense research, including constructions [14,2,16,11], bounds [3,1,15] and generalizations [17,12,13,8]. In this paper, we investigate the maximum achievable rate of locally repairable codes such that reliable transmission is possible over a discrete memoryless channel (DMC).…”
Section: Definitionmentioning
confidence: 99%
“…The last symbol of each group is the modulo-2 sum of the other r symbols. The rate of this code such that the probability of error being vanishing is given by 2…”
Section: Achievabilitymentioning
confidence: 99%
“…Optimal LRCs, meaning LRCs whose global distance attain such bounds, were obtained in [3], [6]- [11], and the first general construction with linear field sizes (i.e., scaling linearly with block length) was obtained in [12]. Recently, optimal LRCs with larger code lengths than the field size were obtained for certain choices of global distance, local distance and/or locality in [13]- [16].…”
Section: Introductionmentioning
confidence: 99%