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- W2951771860 abstract "Let $pge 7$, $q=p^m$. $K_q(a)=sum_{xin mathbb{F}_{p^m}} zeta^{mathrm{Tr}^m_1(x^{p^m-2}+ax)}$ is the Kloosterman sum of $a$ on $mathbb{F}_{p^m}$, where $zeta=e^{frac{2pisqrt{-1}}{p}}$. The value $1-frac{2}{zeta+zeta^{-1}}$ of $K_q(a)$ and its conjugate have close relationship with a class of binomial function with Dillon exponent. This paper first presents some necessary conditions for $a$ such that $K_q(a)=1-frac{2}{zeta+zeta^{-1}}$. Further, we prove that if $p=11$, for any $a$, $K_q(a)neq 1-frac{2}{zeta+zeta^{-1}}$. And for $pge 13$, if $ain mathbb{F}_{p^s}$ and $s=mathrm{gcd}(2,m)$, $K_q(a)neq 1-frac{2}{zeta+zeta^{-1}}$. In application, these results explains some class of binomial regular bent functions does not exits." @default.
- W2951771860 created "2019-06-27" @default.
- W2951771860 creator A5018708611 @default.
- W2951771860 creator A5054829854 @default.
- W2951771860 date "2013-12-26" @default.
- W2951771860 modified "2023-10-03" @default.
- W2951771860 title "Special values of Kloosterman sums and binomial bent functions" @default.
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- W2951771860 doi "https://doi.org/10.48550/arxiv.1312.7191" @default.
- W2951771860 hasPublicationYear "2013" @default.
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