Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CHARACTERIZATION OF CERTAIN TYPES OF r-PLATEAUED FUNCTIONS

  • Hyun, Jong Yoon (Korea Institute for Advanced Study (KIAS)) ;
  • Lee, Jungyun (Department of Mathematics Education Kangwon National University) ;
  • Lee, Yoonjin (Department of Mathematics Ewha Womans University)
  • Received : 2017.11.25
  • Accepted : 2018.01.30
  • Published : 2018.11.01
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Abstract

We study a subclass of p-ary functions in n variables, denoted by ${\mathcal{A}}_n$, which is a collection of p-ary functions in n variables satisfying a certain condition on the exponents of its monomial terms. Firstly, we completely classify all p-ary (n - 1)-plateaued functions in n variables by proving that every (n - 1)-plateaued function should be contained in ${\mathcal{A}}_n$. Secondly, we prove that if f is a p-ary r-plateaued function contained in ${\mathcal{A}}_n$ with deg f > $1+{\frac{n-r}{4}}(p-1)$, then the highest degree term of f is only a single term. Furthermore, we prove that there is no p-ary r-plateaued function in ${\mathcal{A}}_n$ with maximum degree $(p-1){\frac{n-4}{2}}+1$. As application, we partially classify all (n - 2)-plateaued functions in ${\mathcal{A}}_n$ when p = 3, 5, and 7, and p-ary bent functions in ${\mathcal{A}}_2$ are completely classified for the cases p = 3 and 5.

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References

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