A class of almost MDS codes |
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| Institution: | 1. School of Mathematics, Southwest Jiaotong University, Chengdu, 610031, China;2. State Key Laboratory of Cryptology, P. O. Box 5159, Beijing, 100878, China;3. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China;1. Texas A&M University-Commerce, 2200 Campbell Street, Commerce, TX, 75428, USA;2. Department of Mathematics and Statistics, American University of Sharjah, Sharjah, United Arab Emirates;1. School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, China;2. Department of Mathematics, Royal University of Phnom Penh, 12156 Phnom Penh, Cambodia;1. School of Cyber Science and Technology, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, Hubei, China;2. School of Mathematics and Statistics, Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, Hubei, China |
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| Abstract: | MDS codes and almost MDS (AMDS) codes are special classes of linear codes, and have important applications in communications, data storage, combinatorial theory, and secrete sharing. The objective of this paper is to present a class of AMDS codes from some BCH codes and determine their parameters. It turns out the proposed AMDS codes are distance-optimal and dimension-optimal locally repairable codes. The parameters of the duals of this class of AMDS codes are also discussed. |
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| Keywords: | Cyclic code Linear code MDS code BCH code Locally repairable code |
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