Constructions of projective linear codes by the intersection and difference of sets |
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| Affiliation: | 1. School of Science, Chang''an University, Xi''an 710064, China;2. School of Information Engineering, Chang''an University, Xi''an 710064, China;1. School of Computer Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, PR China;2. State Key Laboratory of Integrated Services Networks, Xidian University, Xi''an 710071, PR China;3. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, PR China;4. National Mobile Communications Research Laboratory, Southeast University, 211189, 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;1. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, China;2. State Key Laboratory of Cryptology, P.O. Box 5159, Beijing 100878, China;1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, PR China;2. State Key Laboratory of Cryptology, P.O. Box 5159, Beijing, 100878, PR China;3. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, PR China |
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| Abstract: | Projective linear codes are a special class of linear codes whose dual codes have minimum distance at least 3. Projective linear codes with only a few weights are useful in authentication codes, secret sharing schemes, data storage systems and so on. In this paper, two constructions of q-ary linear codes are presented with defining sets given by the intersection and difference of two sets. These constructions produce several families of new projective two-weight or three-weight linear codes. As applications, our projective codes can be used to construct secret sharing schemes with interesting access structures, strongly regular graphs and association schemes with three classes. |
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| Keywords: | Linear code Projective code Secret sharing scheme Strongly regular graph |
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