The Degree of Balanced Elementary Symmetric Boolean Functions of \bf 4k+\bf 3 Variables.

In this paper, we consider the conjecture that \sigma2^{t+1l-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+1l-1, l odd and 2^t+1\nmid d, \sigman,d is balanced if and only if d=2^k, 1\leq k\leq t. Our results verify most cases of the conjecture for n\equiv3\ (mod\ 4). [ABSTRACT FROM AUTHOR]