On the degree of homogeneous bent functions

In this paper, the degree of homogeneous bent functions is discussed. We prove that for any nonnegative integer kk, there exists a positive integer NN such that for n⩾Nn⩾N there exist no 2n2n- variable homogeneous bent functions having degree n-kn-k or more, where NN is the least integer satisfying 2N-1>N+10+N+11+⋯+N+1k+1.