Nonexistence of two classes of generalized bent functions

We obtain some new nonexistence results of generalized bent functions from $${\mathbb {Z}}^n_q$$Zqn to $${\mathbb {Z}}_q$$Zq (called type [n, q]) in the case that there exist cyclotomic integers in $$ {\mathbb {Z}}[\zeta _{q}]$$Z[ζq] with absolute value $$q^{\frac{n}{2}}$$qn2. This result generalizes two previous nonexistence results $$[n,q]=[1,2\times 7]$$[n,q]=[1,2×7] of Pei (Lect Notes Pure Appl Math 141:165–172, 1993) and $$[3,2\times 23^e]$$[3,2×23e] of Jiang and Deng (Des Codes Cryptogr 75:375–385, 2015). We also remark that by using a same method one can get similar nonexistence results of GBFs from $${\mathbb {Z}}^n_2$$Z2n to $${\mathbb {Z}}_m$$Zm.