Bounds on the Rate of Linear Locally Repairable Codes over Small Alphabets

Abhishek Agarwal; Arya Mazumdar

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arXiv · 1607.08547

Bounds on the Rate of Linear Locally Repairable Codes over Small Alphabets

Abhishek Agarwal·Arya Mazumdar

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Abstract

Locally repairable codes (LRC) have recently been a subject of intense research due to theoretical appeal and their application in distributed storage systems. In an LRC, any coordinate of a codeword can be recovered by accessing only few other coordinates. For LRCs over small alphabet (such as binary), the optimal rate-distance trade-off is unknown. In this paper we provide the tightest known upper bound on the rate of linear LRCs of a given relative distance, an improvement over any previous result, in particular \cite{cadambe2013upper}.

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Abhishek Agarwal, Arya Mazumdar. 2016-07-28. Bounds on the Rate of Linear Locally Repairable Codes over Small Alphabets. https://arxiv.org/abs/1607.08547

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