Nonexistence results on generalized bent functions Zqm→Zq with odd m and q ≡ 2 (mod 4)

• Main Authors: Leung, Ka Hin, Schmidt, Bernhard
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2020
• Subjects: Science::Mathematics; Weil Numbers; Minimal Aliases
• Online Access: https://hdl.handle.net/10356/141391
• Institution: Nanyang Technological University

Let p be an odd prime, let a be a positive integer, let m be an odd positive integer, and suppose that a generalized bent function from Z2pam to Z2pa exists. We show that this implies m≠1, p≤22m+2m+1, and ordp(2)≤2m−1. We obtain further necessary conditions and prove that p=7 if m=3 and p∈{7,23,31,7...