On Cusick-Cheon's Conjecture About Balanced Boolean Functions in the Cosets of the Binary Reed-Muller Code

It is proved an amplification of Cusick-Cheon’s conjecture on balanced Boolean functions in the cosets of the binary Reed-Muller code RM(k,m) of order k and length 2^m, in the cases where k = 1 or k >= (m-1)/2.