Locality via Partially Lifted Codes
نویسندگان
چکیده
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. ∗Computer Science Department, Stanford University. MW’s research is supported in part by NSF grants DMS-1400558 and CCF-1657049. †Computer Science Department, Carnegie Mellon University. Research supported in part by NSF grants CCF-1563742 and CCF-1422045. 1 ar X iv :1 70 4. 08 62 7v 1 [ cs .I T ] 2 7 A pr 2 01 7
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