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Title: Optimal locally repairable codes of distance 3 and 4 via cyclic codes
Authors: Luo, Yuan
Xing, Chaoping
Yuan, Chen
Keywords: Science::Mathematics
Issue Date: 2018
Source: Luo, Y., Xing, C., & Yuan, C. (2019). Optimal locally repairable codes of distance 3 and 4 via cyclic codes. IEEE Transactions on Information Theory, 65(2), 1048-1053. doi:10.1109/TIT.2018.2854717
Journal: IEEE Transactions on Information Theory
Abstract: Like classical block codes, a locally repairable code also obeys the Singleton-type bound (we call a locally repairable code optimal if it achieves the Singleton-type bound). In the breakthrough work of Tamo and Barg, several classes of optimal locally repairable codes were constructed via subcodes of Reed-Solomon codes. Thus, the lengths of the codes given by Tamo and Barg are upper bounded by the code alphabet size q. Recently, it was proved through the extension of construction by Tamo and Barg that the length of q-ary optimal locally repairable codes can be q +1 by Jin et al. Surprisingly, Barg et al. presented a few examples of q-ary optimal locally repairable codes of small distance and locality with code length achieving roughly q 2 . Very recently, it was further shown in the work of Li et al. that there exist q-ary optimal locally repairable codes with the length bigger than q+1 and the distance proportional to n. Thus, it becomes an interesting and challenging problem to construct new families of q-ary optimal locally repairable codes of length bigger than q+1. In this paper, we construct a class of optimal locally repairable codes of distances 3 and 4 with unbounded length (i.e., length of the codes is independent of the code alphabet size). Our technique is through cyclic codes with particular generator and parity-check polynomials that are carefully chosen.
ISSN: 0018-9448
DOI: 10.1109/TIT.2018.2854717
Rights: © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at:
Fulltext Permission: open
Fulltext Availability: With Fulltext
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