Nonexistence of generalized bent functions and the quadratic norm form equations

2018/04/04 by Lv, Chang, Zhu, Yuqing
#11D09 #11D57 #11R29 #94A15 #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1804.01292

Abstract

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.

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