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Paper IDA.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.

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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