Locally recoverable $J$-affine variety codes

Abstract

A locally recoverable (LRC) code is a code over a finite field ${\mathbb{F}}_q$ 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 $\bar{R}$ of positions so that any $\delta -1$ erasures in $\bar{R}$ can be recovered from the remaining $r$ coordinates in this set. We also show that some of these LRC codes with lengths $n\gg q$ are $(\delta -1)$-optimal.

References in corpus (3)

• Binary Cyclic Codes that are Locally Repairable
• New binary and ternary LCD codes
• Classical and Quantum Evaluation Codes at the Trace Roots

Cited by in corpus (1)

• Optimal $(r,\delta )$-LRCs from monomial-Cartesian codes and their subfield-subcodes