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Bounds and Constructions of Codes with Multiple Localities

Abstract : This paper studies bounds and constructions of locally repairable codes (LRCs) with multiple localities so-called multiple-locality LRCs (ML-LRCs). In the simplest case of two localities some code symbols of an ML-LRC have a certain locality while the remaining code symbols have another one. We extend two bounds, the Singleton and the alphabet-dependent upper bound on the dimension of Cadambe–Mazumdar for LRCs, to the case of ML-LRCs with more than two localities. Furthermore, we construct Singleton-optimal ML-LRCs as well as codes that achieve the extended alphabet-dependent bound. We give a family of binary ML-LRCs based on generalized code concatenation that is optimal with respect to the alphabet-dependent bound.
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https://hal.inria.fr/hal-01253384
Contributor : Alexander Zeh Connect in order to contact the contributor
Submitted on : Sunday, January 10, 2016 - 8:32:14 AM
Last modification on : Thursday, January 6, 2022 - 2:50:02 PM
Long-term archiving on: : Monday, April 11, 2016 - 10:52:45 AM

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  • HAL Id : hal-01253384, version 1
  • ARXIV : 1601.02763

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Alexander Zeh, Eitan Yaakobi. Bounds and Constructions of Codes with Multiple Localities. 2016. ⟨hal-01253384⟩

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