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.
Bibliographical noteFunding Information:
Manuscript received May 15, 2017; revised June 24, 2017; accepted July 15, 2017. Date of publication August 2, 2017; date of current version November 9, 2017. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2013R1A1A2062061). The associate editor coordinating the review of this paper and approving it for publication was J. Li. (Corresponding author: Hong-Yeop Song.) The authors are with the Department of Electrical and Electronic Engineering, Yonsei University, Seoul 120-749, South Korea (e-mail: firstname.lastname@example.org). Digital Object Identifier 10.1109/LCOMM.2017.2730183
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All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Computer Science Applications
- Electrical and Electronic Engineering