Nonexistence of two classes of generalized bent functions

Abstract

We obtain new nonexistence results of generalized bent functions from $\{Z^n}_q$ to $\Z_q$ (called type $[n,q]$) in the case that there exist cyclotomic integers in $ \Z[\zeta_{q}]$ with absolute value $q^{\frac{n}{2}}$. This result generalize the previous two scattered nonexistence results $[n,q]=[1,2\times7]$ of Pei \cite{Pei} and $[3,2\times 23^e]$ of Jiang-Deng \cite{J-D} to a generalized class. In the last section, we remark that this method can apply to the GBF from $\Z^n_2$ to $\Z_m$.