Nonexistence of Generalized Bent Functions From $Z_{2}^{n}$ to $Z_{m}$

TL;DR

This paper investigates the nonexistence of generalized bent functions from binary vector spaces to cyclic groups, utilizing cyclotomic number fields and their subfields to establish key nonexistence results.

Contribution

It provides new nonexistence proofs for generalized bent functions using algebraic number theory techniques, extending previous results in the field.

Findings

Nonexistence of certain generalized bent functions from Z_2^n to Z_m.

Application of cyclotomic number fields to prove nonexistence.

Extension of nonexistence results to broader classes of functions.

Abstract

Several nonexistence results on generalized bent functions $f:Z_{2}^{n} \rightarrow Z_{m}$ presented by using some knowledge on cyclotomic number fields and their imaginary quadratic subfields.