On the Single-Parity Locally Repairable Codes with Multiple Repairable Groups
Graduate School at Shenzhen, Tsinghua University, Shenzhen 518055, China
Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China
Author to whom correspondence should be addressed.
Received: 25 September 2018 / Revised: 17 October 2018 / Accepted: 20 October 2018 / Published: 24 October 2018
Locally repairable codes (LRCs) are a new family of erasure codes used in distributed storage systems which have attracted a great deal of interest in recent years. For an
linear code, if a code symbol can be repaired by t
disjoint groups of other code symbols, where each group contains at most r
code symbols, it is said to have availability-
. Single-parity LRCs are LRCs with a constraint that each repairable group contains exactly one parity symbol. For an
single-parity LRC with availability-
for the information symbols (single-parity LRCs), the minimum distance satisfies
. In this paper, we focus on the study of single-parity LRCs with availability-
for information symbols. Based on the standard form of generator matrices, we present a novel characterization of single-parity LRCs with availability
. Then, a simple and straightforward proof for the Singleton-type bound is given based on the new characterization. Some necessary conditions for optimal single-parity LRCs with availability
are obtained, which might provide some guidelines for optimal coding constructions.
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MDPI and ACS Style
Lu, Y.; Liu, X.; Xia, S. On the Single-Parity Locally Repairable Codes with Multiple Repairable Groups. Information 2018, 9, 265.
Lu Y, Liu X, Xia S. On the Single-Parity Locally Repairable Codes with Multiple Repairable Groups. Information. 2018; 9(11):265.
Lu, Yanbo; Liu, Xinji; Xia, Shutao. 2018. "On the Single-Parity Locally Repairable Codes with Multiple Repairable Groups." Information 9, no. 11: 265.
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