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A new construction of rotation symmetric bent functions with maximal algebraic degree

The author is supported by the National Natural Science Foundation of China (Grant No. 61502147) and the Excellent Youth Program of Henan University (Grant No. yqpy20170063)

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  • In this paper, for any even integer $ n = 2m\ge4 $, a new construction of $ n $-variable rotation symmetric bent function with maximal algebraic degree $ m $ is given as

    $ f(x_0,x_1\cdots,x_{n-1}) = \bigoplus\limits_{i = 0}^{m-1}(x_ix_{m+i})\oplus \bigoplus\limits_{i = 0}^{n-1}(x_ix_{i+1}\cdots x_{i+m-2} \overline{x_{i+m}} ), $

    whose dual function is

    $ \widetilde{f}(x_0,x_1\cdots,x_{n-1}) = \bigoplus\limits_{i = 0}^{m-1}(x_ix_{m+i})\oplus \bigoplus\limits_{i = 0}^{n-1}(x_ix_{i+1}\cdots x_{i+m-2} \overline{x_{i+n-2}} ), $

    where $ \overline{x_{i}} = x_{i}\oplus 1 $ and the subscript of $ x $ is modulo $ n $.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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