Two-weight or three-weight binary linear codes from cyclotomic mappings |
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| Institution: | 1. Computer Information Engineering Institute, Jiangxi Normal University, Nanchang 330022, PR China;2. College of Sciences, China University of Petroleum, Qingdao, 266580, PR China;3. School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, ON K1S 5B6, Canada |
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| Abstract: | Recently, linear codes with few weights have been studied extensively. These linear codes have wide applications in secret sharing schemes and authentication codes. In this paper, we introduce a new construction of defining sets using cyclotomic mappings and construct three new classes of binary linear codes with two or three weights. We also explicitly determine the weight distributions of these codes. |
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| Keywords: | Linear codes Secret sharing schemes Weight distribution Defining set Cyclotomic mappings |
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