A note of generalized bent functions

Kumar et al. (1985) introduced the concept of generalized bent functions f:Z(q)(n) --> Z(q) where q is a positive integer > 1, and gave constructions for such functions for every possible value of q and n other than n odd and q = 2 (mod 4). Furthermore, they have shown the non-existence in the remaining case under certain sufficient conditions. The main purpose of this paper is to understand the extent of the set of parameters for which no generalized bent functions exist. In particular, the non-existence of Bent functions on Z(2pr) with p = 7 (mod 8) and r greater than or equal to 1 is examined. The result obtained generalizes recent works of Bi (1991) and Pei (1993).