Binary linear codes from vectorial boolean functions and their weight distribution |
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Authors: | Deng Tang Claude Carlet Zhengchun Zhou |
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Institution: | 1. School of Mathematics, Southwest Jiaotong University, Chengdu, 610031, China;2. LAGA, Department of Mathematics, University of Paris 8 (and Paris 13 and CNRS), Saint–Denis cedex 02, France |
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Abstract: | Binary linear codes with good parameters have important applications in secret sharing schemes, authentication codes, association schemes, and consumer electronics and communications. In this paper, we construct several classes of binary linear codes from vectorial Boolean functions and determine their parameters, by further studying a generic construction developed by Ding et al. recently. First, by employing perfect nonlinear functions and almost bent functions, we obtain several classes of six-weight linear codes which contain the all-one codeword, and determine their weight distribution. Second, we investigate a subcode of any linear code mentioned above and consider its parameters. When the vectorial Boolean function is a perfect nonlinear function or a Gold function in odd dimension, we can completely determine the weight distribution of this subcode. Besides, our linear codes have larger dimensions than the ones by Ding et al.’s generic construction. |
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Keywords: | Vectorial Boolean function Linear code Extended Walsh spectrum Secret sharing scheme Authentication code |
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