Hypergraph-Based Binary Locally Repairable Codes With Availability
Jung Hyun Kim, Hong‐Yeop Song · IEEE Communications Letters · 2017
We study a hypergraph-based code construction for binary locally repairable codes (LRCs) with availability. A symbol of a code is said to have$(r, t)$-availability if it can be recovered from$t$disjoint repair sets of other symbols, each set of size at most$r$. We refer a systematic code to an LRC with$(r, t)_{i}$-availability if its information symbols have$(r, t)$-availability and a code to an LRC with$(r, t)_{a}$-availability if its all symbols have$(r, t)$-availability. We construct binary LRCs with$(r, t)_{i}$-availability from linear$r$-uniform$t$-regular hypergraphs. As a special case, we also construct binary LRCs with$(r, t)_{a}$-availability from labeled linear$r$-uniform$t$-regular hypergraphs. Moreover, we extend the hypergraph-based codes to increase the minimum distance. All the proposed codes achieve a well-known Singleton-like bound with equality.