More constructions of semi-bent and plateaued functions in polynomial forms

Plateaued functions and their subclass semi-bent functions have useful applications in cryptography and communications. In this paper we give new constructions of quadratic semi-bent functions in polynomial forms on the finite field F2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_{2^n}$$\end{document} for both odd and even n. We also present some characterizations of e-plateaued functions with few trace terms when n is even.