Locally recoverable J-affine variety codes

Abstract

A locally recoverable (LRC) code is a code over a finite eld Fq such that any erased coordinate of a codeword can be recovered from a small number of other coordinates in that codeword. We construct LRC codes correcting more than one erasure, which are sub eld-subcodes of some J-affine variety codes. For these LRC codes, we compute localities (r; )) that determine the minimum size of a set R of positions so that any - 1 erasures in R can be recovered from the remaining r coordinates in this set. We also show that some of these LRC codes with lengths n >> q are ( - 1)-optimal.