New nonexistence results on $(m,n)$-generalized bent functions

Abstract

In this paper, we present some new nonexistence results on $(m,n)$-generalized bent functions, which improved recent results. More precisely, we derive new nonexistence results for general $n$ and $m$ odd or $m\equiv 2(\mathrm{mod}4)$, and further explicitly prove nonexistence of $(m,3)$-generalized bent functions for all integers $m$ odd or $m\equiv 2(\mathrm{mod}4)$. The main tools we utilized are certain exponents of minimal vanishing sums from applying characters to group ring equations that characterize $(m,n)$-generalized bent functions.