The highly nonlinear odd-dimensional Boolean-functions have many applications in the cryptographic practice, that is why the
research of that function-classes and construction of such functions have a great importance. This study focuses on some types
of functions having special characteristics in the class of highly nonlinear odd-dimensional Boolean-functions. Upper bound
can be given for the number of non-zero linear structures of such functions and regarding them as mappings some functional-relations
can be proved. From the results one can gain two algorithms. By the help of the first one special highly nonlinear odd dimensional
Boolean-functions can be constructed by using functions having the same characteristics, the second one renders possible the
construction of bent functions of a one-level higher dimension by the use of special highly nonlinear odd-dimensional Boolean-functions.
The paper shows a relation between bent functions in even dimensional Boolean-space and odd dimensional highly nonlinear Boolean