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- W2000663911 abstract "Based on a computer search, Anne Canteaut conjectured that the exponent $2^{2r}+2^r+1$ in ${bf F}_{2^{6r}}$ and the exponent $(2^{r}+1)^2$ in ${bf F}_{2^{4r}}$ yield bent monomial functions. These conjectures are proved in [A. Canteaut, P. Charpin, and G. Kyureghyan, A new class of monomial bent functions, in Proceedings of the 2006 IEEE International Symposium on Information Theory, (ISIT 06 Seattle), IEEE Press, Piscataway, NJ, 2006, pp. 903–906] and [N. G. Leander, IEEE Trans. Inform. Theory, 52 (2006), pp. 738–743]. Both exponents are of binary weight 3 and define functions from the Maiorana–McFarland class $mathcal{M}$ of bent functions to the subfield. In this paper we show that these are the only such exponents. Our proof is based on the classification of the permutation binomials $X^{2^k+2}+ nu X$ of finite fields of even characteristics. We also extend the result of Leander, determining all bent monomial functions with the exponent $(2^{r}+1)^2$." @default.
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- W2000663911 date "2008-01-01" @default.
- W2000663911 modified "2023-09-25" @default.
- W2000663911 title "Cubic Monomial Bent Functions: A Subclass of $mathcal{M}$" @default.
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- W2000663911 doi "https://doi.org/10.1137/060677768" @default.
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