New algebraic and combinatorial constructions for optimal frequency hopping sequence sets

In this paper, four algebraic and combinatorial constructions for optimal frequency-hopping sequence (FHS) sets employing additive groups of finite fields, u-flats in projective geometries and difference sets are presented. The constructions produce three new families of optimal FHS sets achieving the Peng-Fan bound. One of the proposed constructions generalizes the previous constructions of optimal FHS sets using m-sequences. In addition, some other FHS sets can be obtained via the well-known recursive constructions.