The nonexistance of homogeneous bent functions of degree n in 2n variables for n > 3 was analyzed. For the analysis, a certain decomposition of a Menon difference set, which corrosponds to bent function was used. The results show that there is no homogeneous bent function of degree 4 in 8 Boolean variables. However, it was suggested that there are few execeptions such as 3-homogeneous Boolean functions of 6 variables, and the 2-homogeneous Boolean functions of 4 variables.
- Difference sets