2020 IEEE International Symposium
on Information Theory
21-26 June 2020 • Los Angeles, California, USA
| Paper ID | A.1.2 | ||
| Paper Title | Optimal Locally Repairable Constacyclic Codes of Prime Power Lengths | ||
| Authors | Wei Zhao, The Chinese University of Hong Kong, Shenzhen; University of Science and Technology of China, China; Kenneth W. Shum, Shenghao Yang, The Chinese University of Hong Kong, Shenzhen, China | ||
| Session | A.1: Algebraic Coding Theory I | ||
| Presentation | Lecture | ||
| Track | Algebraic and Combinatorial Coding Theory | ||
| Manuscript | Click here to download the manuscript | ||
| Virtual Presentation | Click here to watch in the Virtual Symposium | ||
| Abstract | A locally repairable code (LRC) with locality r allows for the recovery of any erased symbol of a codeword by accessing only r other symbols of the same codeword. The LRCs achieving the Singleton-like bound are said to be optimal. In this paper, we completely characterize the locality of any constacyclic codes of length p^s over finite fields. Using this characterization, we determine all the optimal constacyclic LRCs of prime power lengths over finite fields, i.e., there are no other optimal constacyclic LRCs of prime power length except for those we characterized in this paper. We classify all the optimal constacyclic LRCs into seven classes. The first six classes of constacyclic LRCs classified in this paper have unbounded length, and can achieve smaller locality comparing to those codes constructed by Luo, Xing and Yuan, which also provide unbounded length. | ||
Plan Ahead
2021 IEEE International Symposium on Information Theory
11-16 July 2021 | Melbourne, Victoria, Australia
