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

## TL;DR

This paper establishes new nonexistence results for $(m,n)$-generalized bent functions, especially for odd $n$ and specific $m$ congruences, using character sum techniques.

## Contribution

It improves existing nonexistence results by deriving new conditions for the nonexistence of $(m,n)$-generalized bent functions, including explicit cases for $n=3$.

## Key findings

- Nonexistence of $(m,n)$-generalized bent functions for odd $n$ and certain $m$
- Explicit nonexistence of $(m,3)$-generalized bent functions for specific $m$
- Use of character sums and group ring equations as main tools

## 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 $m \equiv 2 \pmod{4}$, and further explicitly prove nonexistence of $(m,3)$-generalized bent functions for all integers $m$ odd or $m \equiv 2 \pmod{4}$. 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.