Locally recoverable J-affine variety codes

摘要

A locally recoverable (LRC) code is a code over a finite field F-q 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 subfield-subcodes of some J-affine variety codes. For these LRC codes, we compute localities (r, delta) that determine the minimum size of a set (R) over bar of positions so that any delta - 1 erasures in (R) over bar 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 (delta - 1)-optimal. (C) 2020 Elsevier Inc. All rights reserved.