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arXiv · 1704.08627

Locality via Partially Lifted Codes

S. Luna Frank-Fischer·Venkatesan Guruswami·Mary Wootters
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Abstract

In error-correcting codes, locality refers to several different ways of quantifying how easily a small amount of information can be recovered from encoded data. In this work, we study a notion of locality called the s-Disjoint-Repair-Group Property (s-DRGP). This notion can interpolate between two very different settings in coding theory: that of Locally Correctable Codes (LCCs) when s is large---a very strong guarantee---and Locally Recoverable Codes (LRCs) when s is small---a relatively weaker guarantee. This motivates the study of the s-DRGP for intermediate s, which is the focus of our paper. We construct codes in this parameter regime which have a higher rate than previously known codes. Our construction is based on a novel variant of the lifted codes of Guo, Kopparty and Sudan. Beyond the results on the s-DRGP, we hope that our construction is of independent interest, and will find uses elsewhere.

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S. Luna Frank-Fischer, Venkatesan Guruswami, Mary Wootters. 2017-04-27. Locality via Partially Lifted Codes. https://arxiv.org/abs/1704.08627

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