New nonexistence results on (m,n)-generalized bent functions

2019/08/02 by Ka Hin Leung, Qi Wang, Leung, Ka Hin +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #graph theory and CDMA systems #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1908.00842

Abstract

In this paper, we present some new nonexistence results on (m,n)-generalized bent functions, which improved recent results. More precisely, we derive new nonexistence results for general n and m odd or m ≡ 2 \pmod4, and further explicitly prove nonexistence of (m,3)-generalized bent functions for all integers m odd or m ≡ 2 \pmod4. The main tools we utilized are certain exponents of minimal vanishing sums from applying characters to group ring equations that characterize (m,n)-generalized bent functions.

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