On Balanced Semi-Bent Functions with High Algebraic Degrees

A class of balanced semi-bent functions with an even number of variables is proposed. It is shown that they include one subclass of semi-bent functions with maximum algebraic degrees. Furthermore, an example of semi-bent functions in a small field is given by using the zeros of some Kloosterman sums. Based on the result given by S. Kim et al., an example of infinite families of semi-bent functions is also obtained.