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On the constructions of MDS self-dual codes via cyclotomy
Affiliation:1. Department of Mathematical Sciences, Xi''an University of Technology, Shannxi, 710054, China;2. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China;1. Applied Algebra and Optimization Research Center, Sungkyunkwan University, Suwon, Republic of Korea;2. Institute of Mathematical Sciences, Ewha Womans University, Seoul, Republic of Korea;1. School of Mathematics, HeFei University of Technology, Hefei 230009, China;2. Intelligent Interconnected Systems Laboratory of Anhui Province Hefei, China;1. School of Mathematics, Southwest Jiaotong University, Chengdu, 610031, China;2. Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;1. Faculty of Mathematics USTHB, University of Science and Technology of Algiers, Algeria;2. Department of Mathematics, HTTC Bertoua, The University of Ngaoundéré, Cameroon;3. Institute of Mathematics, University of Valladolid, Castilla, Spain
Abstract:MDS self-dual codes over finite fields have attracted a lot of attention in recent years by their theoretical interests in coding theory and applications in cryptography and combinatorics. In this paper we present a series of MDS self-dual codes with new length by using generalized Reed-Solomon codes and extended generalized Reed-Solomon codes as the candidates of MDS codes and taking their evaluation sets as a union of cyclotomic classes. The conditions on such MDS codes being self-dual are expressed in terms of cyclotomic numbers.
Keywords:MDS codes  Self-dual codes  Generalized Reed-Solomon codes  Cyclotomic number
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