Weight distributions and weight hierarchies of two classes of binary linear codes |
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| Affiliation: | 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. 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. School of Mathematical Sciences, 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;4. College of Mathematics and Physics, Yancheng Institute of Technology, Yancheng, 224003, China;5. School of Mathematical Sciences, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China;1. College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, PR China;2. School of Mathematics and Statistics, Zaozhuang University, Zaozhuang, 277160, PR China;1. Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, China;2. Wuhan Maritime Communication Research Institute, Wuhan 430079, China |
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| Abstract: | Linear codes with a few weights can be applied to communication, consumer electronics and data storage system. In addition, the weight hierarchy of a linear code has many applications such as on the type II wire-tap channel, dealing with t-resilient functions and trellis or branch complexity of linear codes and so on. In this paper, we present a formula for computing the weight hierarchies of linear codes constructed by the generalized method of defining sets. Then, we construct two classes of binary linear codes with a few weights and determine their weight distributions and weight hierarchies completely. Some codes of them can be used in secret sharing schemes. |
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| Keywords: | Weight distribution Weight hierarchy Linear code Generalized Hamming weight |
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