This volume contains the refereed proceedings papers of the Fifth International ConferenceonSequencesandtheirApplications(SETA2008), heldinLexington, Kentucky (USA), September 14-18, 2008. The conference SETA is well est- lished in the mathematics and computer science community. Topics of "SETA" include - Randomness of sequences - Correlation (periodic and aperiodic types) and combinatorial aspects of - quences (di?erence sets) - Sequences with applications in coding theory and cryptography - Sequences over ?nite ?elds/rings/function ?elds - Linear and nonlinear feedback shift register sequences - Sequences for radar distance ranging, synchronization, identi?cation, and hardware testing - Sequences for wireless communication - Pseudorandom sequence generators - Correlation and transformation of Boolean functions - Multidimensional sequences and their correlation properties - Linear and nonlinear complexity of sequences. This year's proceedings contain 32 contributed papers. All papers have been thoroughly refereed by at least two referees. Most of the refereeing was done by members of the program committee. We thank all of them for their help. We arealsogratefultoSerdarBozta, s, Nina Brandst] atter, Nicolas Courtois, Fa- wei Fu, Honggang Hu, Alexander Kholosha, Emmanuel Prou?, Martin Ro ]tteler, Ayineedi Venkateswarlu and Bo-Yin Yang for their assistance in the reviewing process. In addition to the contributed papers, we had four invited lectures given by Claude Carlet (University of Paris 8, France), Pierre L'Ecuyer (Universitede Montr eal, Canada), Guang Gong (University of Waterloo, Canada) and Robert McEliece (California Institute of Technology, USA). You ?nd papers based on these invited talks in this volume."

Difference sets are of central interest in finite geometry and design theory. One of the main techniques to investigate abelian difference sets is a discrete version of the classical Fourier transform (i.e., character theory) in connection with algebraic number theory. This approach is described using only basic knowledge of algebra and algebraic number theory. It contains not only most of our present knowledge about abelian difference sets, but also gives applications of character theory to projective planes with quasiregular collineation groups. Therefore, the book is of interest both to geometers and mathematicians working on difference sets. Moreover, the Fourier transform is important in more applied branches of discrete mathematics such as coding theory and shift register sequences.