On decomposition of a Boolean function into sum of bent functions

In the paper, some new results on bent sum decomposition problem are discussed. It is proved that any Boolean function in $n$ variables of degree $d\leq n/2$ can be represented as the sum of not more than $2{2b\choose b}$ bent functions, where $b\geq d$ and $b$ is the least integer such that $2b|n$.