Nonexistence of generalized bent functions and the quadratic norm form equations
It provides a universal nonexistence result for a large class of generalized bent functions, advancing the theoretical understanding of these cryptographic objects.
The paper proves the nonexistence of generalized bent functions of type [n, 2p^e] for odd primes p under certain inequalities, using quadratic norm form equations and computational methods under the Generalized Riemann Hypothesis.
We present a new result on the nonexistence of generalized bent functions (GBFs)from (Z/tZ)^n to Z/tZ (called type [n, t]) for a large class. Assume p is an odd prime number. By showing certain quadratic norm form equations having no integral points, we obtain a universalresult on the nonexistence of GBFs with type [n,2p^e] when p and n satisfy a certain inequality, and by computational methods with a widely accepted hypothesis, Generalized Riemann Hypothesis, we also achieve some results on the nonexistence of GBFs for relatively small p.