The Degree of Balanced Elementary Symmetric Boolean Functions of ${{\bf 4k}+{\bf 3}}$ Variables
Guangpu Gao, Wenfen Liu, Xiyong Zhang · IEEE Transactions on Information Theory · 2011
In this paper, we consider the conjecture that σ2t+1l-1,2tare the only nonlinear balanced elementary symmetric Boolean functions wheretandlare positive integers. We prove ifn=2t+1l-1,lodd and 2t+1 midd, σn,dis balanced if and only ifd=2k, 1 ≤k≤t. Our results verify most cases of the conjecture forn≡ 3 (mod 4) .