Two classes of p-ary bent functions and linear codes with three or four weights

In this paper, a secondary construction of p-ary bent functions is presented. Two classes of p-ary bent functions of algebraic degree p are constructed by modifying the values of some known bent functions on some set of Fp2k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb {F}_{p^{2k}}$\end{document}. Furthermore, the resulted p-ary bent functions are employed to construct a class of linear codes with three or four weights.