Mathematics

CLC number: O 156.1

A Class of n-to-1 Binomials over Finite Fields

¹ School of Mathematics and Big Data, Chongqing University of Education, Chongqing 400065, China
² School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China

^† To whom correspondence should be addressed. E-mail: yanl930@163.com

Received: 22 June 2022

Abstract

$n$-to-1 mappings have many applications in combinatorial design, coding theory and cryptography. In this paper, by using piecewise method and monomials on subsets of $q+\mathrm{1}$-th roots of unity, we show a class of $n$-to-1 binomials having the form $x^r(a+x^{s(q-\mathrm{1})})$ over $F_{q^{\mathrm{2}}}$.