@article{fb0713916109401b9330d51c1c922abf,
title = "On Optimal Locally Repairable Codes with Super-Linear Length",
abstract = "In this paper, locally repairable codes which have optimal minimum Hamming distance with respect to the bound presented by Prakash et al. are considered. New upper bounds on the length of such optimal codes are derived. The new bounds apply to more general cases, and have weaker requirements compared with the known ones. In this sense, they both improve and generalize previously known bounds. Further, optimal codes are constructed, whose length is order-optimal with respect to the new upper bounds. Notably, the length of the codes is super-linear in the alphabet size.",
keywords = "Distributed storage, Steiner systems, locally repairable codes, packings",
author = "Han Cai and Ying Miao and Moshe Schwartz and Xiaohu Tang",
note = "Funding Information: Manuscript received February 3, 2019; revised October 31, 2019; accepted January 29, 2020. Date of publication March 2, 2020; date of current version July 14, 2020. The work of Han Cai and Moshe Schwartz was supported by the German Israeli Project Cooperation (DIP) under Grant PE2398/1-1. The work of Ying Miao was supported by the JSPS Grant-in-Aid for Scientific Research (B) under Grant 18H01133. The work of Xiaohu Tang was supported by the National Natural Science Foundation of China under Grant 61871331. This article was presented in part at the 2019 IEEE International Symposium on Information Theory. (Corresponding author: Han Cai.) Han Cai and Moshe Schwartz are with the School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer Sheva 8410501, Israel (e-mail: hancai@aliyun.com; schwartz@ee.bgu.ac.il). Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",
year = "2020",
month = aug,
day = "1",
doi = "10.1109/TIT.2020.2977647",
language = "English",
volume = "66",
pages = "4853--4868",
journal = "IEEE Transactions on Information Theory",
issn = "0018-9448",
publisher = "Institute of Electrical and Electronics Engineers",
number = "8",
}