Optimal frequency hopping sequences

The purpose of this thesis is constructing Optimal Frequency Hopping Sequences (FHSs)which are used in popular systems such as Frequency Hopping-Code Division Multiple Access(FH-CDMA), Bluetooth and Ultra-Wide Band. There are bounds in literature determining optimality.The optimality here is by means of Lempel-Greenberger and Peng-Fan. In this thesis,construction methods of optimal FHSs published since 1974 are analysed and gathered in atable. In addition, so as to examine the sharpness of Lempel-Greenberger Bound, the optimalitybound and its proof given in the paper published in 1974 take place. There are severalmethods for constructing optimal FHSs like algebraic, combinatorial e.t.c.. Four papers givingalgebraic construction via trace function are analysed and their examples are builded by implementingconstruction methods in MAGMA. Additionally, a MAGMA code is implemented inorder to construct FHSs for entered parameters and new existing optimal FHSs are searched.There are optimal FHSs for some fixed parameters, but there is not captured any pattern yet.Our search for optimal FHS construction is not finished. In our future study, we are planningto do the same study that we have done for Trace function for other techniques.