Please use this identifier to cite or link to this item:
https://hdl.handle.net/10356/143232
Title: | Optimal locally repairable codes via elliptic curves | Authors: | Li, Xudong Ma, Liming Xing, Chaoping |
Keywords: | Science::Mathematics | Issue Date: | 2018 | Source: | Li, X., Ma, L., & Xing, C. (2019). Optimal locally repairable codes via elliptic curves. IEEE Transactions on Information Theory, 65(1), 108-117. doi:10.1109/TIT.2018.2844216 | Journal: | IEEE Transactions on Information Theory | Abstract: | Constructing locally repairable codes achieving Singleton-type bound (we call them optimal codes in this paper) is a challenging task and has attracted great attention in the last few years. Tamo and Barg first gave a breakthrough result in this topic by cleverly considering subcodes of Reed-Solomon codes. Thus, q-ary optimal locally repairable codes from subcodes of Reed-Solomon codes given by Tamo and Barg have length upper bounded by q. Recently, it was shown through extension of construction by Tamo and Barg that length of q-ary optimal locally repairable codes can be q+1 by Jin et al.. Surprisingly it was shown by Barg et al. that, unlike classical MDS codes, q-ary optimal locally repairable codes could have length bigger than q+1. Thus, it becomes an interesting and challenging problem to construct q-ary optimal locally repairable codes of length bigger than q+1. In this paper, we make use of rich algebraic structures of elliptic curves to construct a family of q-ary optimal locally repairable codes of length up to q+2√(q). It turns out that locality of our codes can be as big as 23 and distance can be linear in length. | URI: | https://hdl.handle.net/10356/143232 | ISSN: | 0018-9448 | DOI: | 10.1109/TIT.2018.2844216 | Schools: | School of Physical and Mathematical Sciences | 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: https://doi.org/10.1109/TIT.2018.2844216. | Fulltext Permission: | open | Fulltext Availability: | With Fulltext |
Appears in Collections: | SPMS Journal Articles |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Optimal Locally Repairable Codes Via Elliptic Curves.pdf | 264.16 kB | Adobe PDF | View/Open |
SCOPUSTM
Citations
5
63
Updated on Mar 18, 2024
Web of ScienceTM
Citations
10
51
Updated on Oct 26, 2023
Page view(s)
230
Updated on Mar 18, 2024
Download(s) 50
118
Updated on Mar 18, 2024
Google ScholarTM
Check
Altmetric
Items in DR-NTU are protected by copyright, with all rights reserved, unless otherwise indicated.