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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...
In this paper, we propose two upper bounds for locally repairable codes (LRCs) with joint locality. The bounds take into account the code length, dimension, minimum distance, joint locality, and field size, i.e., the size of code alphabet. We also introduce binary linear LRCs designed by utilizing simple graphs. Some of them with certain choice of parameters achieve both of the bounds simultaneously...
In this paper, we propose a construction of binary locally repairable codes from complete multipartite graphs. Our codes possess joint locality (r1 = 2, r2 = 3 or 4). Joint locality is a set of numbers of symbols for repairing various erasure patterns of symbols. We also provide availability properties of our codes. A code is said to have (r, t)-availability if each of its symbols can be repaired...
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