A family of codes with variable locality and availability

TL;DR

This paper introduces a new class of locally recoverable codes with variable recovery options and multiple recovery sets, enhancing data resilience and flexibility in error correction.

Contribution

It defines a novel family of codes with variable locality and availability, allowing multiple recovery sets and robustness against erasures within recovery groups.

Findings

Codes support multiple, distinct recovery sets for each position

Recovery is possible despite erasures in some recovery set entries

The class generalizes existing locally recoverable codes with variable parameters

Abstract

In this work we present a class of locally recoverable codes, i.e. codes where an erasure at a position $P$ of a codeword may be recovered from the knowledge of the entries in the positions of a recovery set $R_P$. The codes in the class that we define have availability, meaning that for each position $P$ there are several distinct recovery sets. Also, the entry at position $P$ may be recovered even in the presence of erasures in some of the positions of the recovery sets, and the number of supported erasures may vary among the various recovery sets.