Several classes of bent, near-bent and 2-plateaued functions over finite fields of odd characteristic

Inspired by a recent work of Mesnager, we present several new infinite families of quadratic ternary bent, near-bent and 2-plateaued functions from some known quadratic ternary bent functions. Meanwhile, the distribution of the Walsh spectrum of two class of 2-plateaued functions obtained in this paper is completely determined. Additionally, we construct the first class of p-ary bent functions of algebraic degree p over the fields of an arbitrary odd characteristic. The proposed class contains non-quadratic p-ary bent functions that are affinely inequivalent to known monomial and binomial ones.