The Degree of Balanced Elementary Symmetric Boolean Functions of 4K+3 Variables
In this paper, we consider the conjecture that sigma(t+1)(2) l-1,2(t) are the only nonlinear balanced elementary symmetric Boolean functions where t and l are positive integers. We prove if n = 2(t+1) l - 1, l odd and 2(t+1) (sic) d, sigma(n,d) is balanced if and only if d = 2(k), 1 <= k <= t. Our results verify most cases of the conjecture for n equivalent to 3 (mod 4).
elementary symmetric boolean functions algebraic degree balancedness lucas' theorem