Linear codes from vectorial Boolean power functions |
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| Institution: | 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. Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, China;2. School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, K1S 5B6, Canada;1. School of Science, Chang''an University, Xi''an 710064, China;2. Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China |
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| Abstract: | In this paper, three classes of binary linear codes with few weights are proposed from vectorial Boolean power functions, and their weight distributions are completely determined by solving certain equations over finite fields. In particular, a class of simplex codes and a class of first-order Reed-Muller codes can be obtained from our construction by taking the identity map, whose dual codes are Hamming codes and extended Hamming codes, respectively. |
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| Keywords: | Vectorial Boolean power function Linear code Weight distribution |
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