@article{Bajrić2022, 
author = {Samed Bajrić},
title = {On a class of bent, near-bent, and 2-plateaued functions over finite fields of odd characteristic},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {2},
pages = {1971-1981},
keywords = {Fourier transform, p-ary functions, nonbinary finite field, s-plateaued, near-bent functions},
url = {https://www.sciopen.com/article/10.3934/math.2022113},
doi = {10.3934/math.2022113},
abstract = {The main purpose of this paper is to study a class of the    p-ary functions        f          λ      ,      u      ,      v        (  x  )  =  T      r    1    k    (  λ      x                  p        k            +      1        )  +  T      r    1    n    (  u  x  )  T      r    1    n    (  v  x  ) for any odd prime    p and    n  =  2  k  ,  λ  ∈  G  F  (      p    k        )    ∗    ,  u  ,  v  ∈  G  F  (      p    n        )    ∗    . With the help of Fourier transforms, we are able to subdivide the class of all        f          λ      ,      u      ,      v       into sublcasses of bent, near-bent and 2-plateaued functions. It is shown that the choice of    λ  ,  u and    v, ensuring that    f is bent, 2-plateaued or near-bent, is directly related to finding the subset    A  ⊂  G  F  (  p      )    3  . The efficient method for defining the set    A  ⊂  G  F  (  p      )    3   is described in detail.}
}