New classes of optimal ternary cyclic codes with minimum distance four |
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| Affiliation: | 1. School of Mathematical Sciences, Henan Key Laboratory of Big Data Processing and Analysis, Luoyang Normal University, Luoyang 471934, China;2. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China;3. School of Cyber Security, University of Chinese Academy of Sciences, Beijing 100049, China;1. Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China;2. PCL Research Center of Networks and Communications, Peng Cheng Laboratory, Shenzhen 518055, China;3. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, China;4. Tianjin Key Laboratory of Network and Data Security Technology, Nankai University, Tianjin 300071, China;1. Departamento de Matemática, Universidade Federal de Minas Gerais, UFMG, Belo Horizonte, MG, 30123-970, Brazil;2. Departamento de Matemática, Universidade Federal de Roraima, UFRR, Boa Vista, RR, 69304-000, Brazil;1. Faculty of School of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu, Anhui Province, 233030, PR China;2. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, PR China;1. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Viet Nam;2. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China;3. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam;4. School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei 430079, China;5. Centre of Excellence in Econometrics, Faculty of Economics, Chiang Mai University, Chiang Mai 52000, Thailand;1. Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China;2. State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing 100093, China;3. Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing 100048, China |
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| Abstract: | Cyclic code is an interesting topic in coding theory and communication systems. In this paper, we investigate the ternary cyclic codes with parameters based on some results proposed by Ding and Helleseth in 2013. Six new classes of optimal ternary cyclic codes are presented by determining the solutions of certain equations over . |
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| Keywords: | Cyclic codes Finite fields Irreducible polynomials Sphere packing bound |
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