Optimal frequency hopping sequences: a combinatorial approach

Frequency hopping multiple access (FHMA) spread-spectrum communication systems employing multiple frequency-shift keying (MFSK) as data modulation technique are investigated from a combinatorial approach. A correspondence between optimal frequency hopping (FH) sequences and partition-type difference packings is first established. By virtue of this correspondence, FHMA systems with a single optimal FH sequence each are constructed from various combinatorial structures such as affine geometries, cyclic designs, and difference families. Combinatorial recursive constructions are also presented. Many new infinite series of optimal FH sequences are thus obtained. These new FH sequences are also useful in ultra wideband (UWB) communication systems.     

Optimal authentication systems and combinatorial designs

In 1982, G.J. Simmons introduced a mathematical model of authentication theory. Recently, E.F. Brickell (1984) and D.R. Stinson (1988) have shown some combinatorial constructions for optimal authentication systems. In the present work, game-theoretical models are proposed for authentication systems that have multilevel costs on sources, and lower bounds of the game values are obtained. Some constructions of the optimal authentication systems that attain the bounds are shown     

Sets of Frequency Hopping Sequences: Bounds and Optimal Constructions

Frequency hopping spread spectrum and direct sequence spread spectrum are two main spread coding technologies in communication systems. Frequency hopping sequences are needed in frequency hopping code-division multiple-access (FH-CDMA) systems. In this paper, four algebraic and a combinatorial constructions of optimal sets of frequency hopping sequences with new parameters are presented, and a number of bounds on sets of frequency hopping sequences are described.