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• W2900500378 abstract "Let <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$Bbb F_{p}$ </tex-math></inline-formula> be a finite field with <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$p$ </tex-math></inline-formula> elements, where <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$p$ </tex-math></inline-formula> is a prime. Let <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$N ge 2$ </tex-math></inline-formula> be an integer and <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$d$ </tex-math></inline-formula> be the least positive integer satisfying <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$p^{d} equiv -1 pmod N$ </tex-math></inline-formula> . Let <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$q = p^{2sd}$ </tex-math></inline-formula> for some integers <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$s$ </tex-math></inline-formula> . In some special cases, we obtain the explicit evaluation of the following exponential sums: <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$S(a,b)=sum _{xin Bbb F_{q}^{*}}zeta _{p}^{ mathrm {Tr}_{q/p}(ax^{(({q-1})/{N})}+bx)}$ </tex-math></inline-formula> . As applications, Walsh spectrums of the monomial functions <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink> <tex-math notation=LaTeX>$mathrm {Tr}_{q/p}(x^{(({q-1})/{N})})$ </tex-math></inline-formula> in three cases are investigated. Our results show that Walsh spectrums of the monomial functions have at most four, five, or seven distinct values. Furthermore, three families of the monomial functions with three-valued Walsh spectrums are presented, see <xref ref-type=corollary rid=corollary12 xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>Corollaries 12</xref> , <xref ref-type=corollary rid=corollary21 xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>21</xref> , <xref ref-type=corollary rid=corollary31 xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>31</xref> , and <xref ref-type=corollary rid=corollary32 xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>32</xref> . Consequently, certain previously known results by Li and Yue and Moisio are extended." @default.
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• W2900500378 date "2019-05-01" @default.
• W2900500378 modified "2023-10-16" @default.
• W2900500378 title "Three Families of Monomial Functions With Three-Valued Walsh Spectrum" @default.
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