On the Non-existence of certain classes of generalized bent functions

TL;DR

This paper establishes new non-existence results for certain classes of generalized bent functions, specifically for functions from ZZ^n_q to ZZ_q, expanding the understanding of their mathematical limitations.

Contribution

It provides the first non-existence proofs for specific classes of generalized bent functions with particular modulus structures, advancing theoretical knowledge in this area.

Findings

Non-existence for q=2p_1^{r_1}p_2^{r_2} cases

Non-existence for types [1 <= n <= 3, 2 * 31^e]

Non-existence for types [1 <= n <= 7, 2 * 151^e]

Abstract

We obtain new non-existence results of generalized bent functions from \ZZ^n_q to \ZZ_q (called type [n,q]). The first case is a class of types where q=2p_1^{r_1}p_2^{r_2}. The second case contains two types [1 <= n <= 3, 2 * 31^e]$ and [1 <= n <= 7,2 * 151^e].