On the sets of the propagation criterion for strict majority Boolean functions

In this paper we investigate the propagation criterion for strict majority symmetric Boolean functions. With the use of the theory of Krawtchouk polynomials it is shown that vectors whose Hamming weight differs from $n/2$ by at most $1/2$ satisfy the propagation criterion for strict majority functions in $n$ variables, where $\lfloor n/2\rfloor$ is odd.