On a class of binomial bent functions over the finite fields of odd characteristic

摘要

We give a necessary and sufficient condition such that the class of (p)-ary binomial functions proposed by Jia et al. (IEEE Trans Inf Theory 58(9):6054–6063, 2012) are regular bent functions, and thus settle the open problem raised at the end of that paper. Moreover, we investigate the bentness of the proposed binomials under the case (gcd (frac{t}{2}, p^{frac{n}{2}}+1)=1) for some even integers (t) and (n). Computer experiments show that the new class contains bent functions that are affinely inequivalent to known monomial and binomial ones.