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- W2343431952 abstract "Bent functions are of great importance in both mathematics and information science. The $mathcal{P}mathcal{S}$ class of bent functions was introduced by Dillon in 1974, but functions belonging to this class that can be explicitly represented are only the $mathcal{P}mathcal{S}_{text{ap}}$ functions, which were also constructed by Dillon after his introduction of the $mathcal{P}mathcal{S}$ class. In this paper, a technique of using finite pre-quasifield spread from finite geometry to construct $mathcal{P}mathcal{S}$ bent functions is proposed. The constructed functions are in similar styles with the $mathcal{P}mathcal{S}_{text{ap}}$ functions. To explicitly represent them in bivariate forms, the main task is to compute compositional inverses of certain parametric permutation polynomials over finite fields of characteristic 2. Concentrated on the Dempwolff-Muller pre-quasifield, the Knuth pre-semifield and the Kantor pre-semifield, three new subclasses of the $mathcal{P}mathcal{S}$ class are obtained. They are the only sub-classes that can be explicitly constructed more than 30 years after the $mathcal{P}mathcal{S}_{text{ap}}$ subclass was introduced." @default.
- W2343431952 created "2016-06-24" @default.
- W2343431952 creator A5046374199 @default.
- W2343431952 date "2013-08-15" @default.
- W2343431952 modified "2023-09-27" @default.
- W2343431952 title "$mathcal{P}mathcal{S}$ bent functions constructed from finite pre-quasifield spreads" @default.
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