The concept of thickness assigns to every Cantor set in the real line a number from 0 to [infinity symbol]. It was known that for some pairs of numbers the intersection of Cantor sets with such numbers as thicknesses may be just one point and that, in some other cases, with cert…
Difference sets belong both to group theory and to combinatorics. Studying them requires tools from geometry, number theory, and representation theory. This book lays a foundation for these topics, including a primer on representations and characters of finite groups. It makes t…
1. Mathematical foundations. 1.1. Group actions. 1.2. The rings Zn. 1.3. Finite fields. 1.4. Cyclotomy in GF(r ). 1.5. Generalized cyclotomy in Zn[symbols]. 1.6. Finite geometries. 1.7. Planar functions. 1.8. Periodic sequences -- 2. Linear codes over finite fields. 2.1. Linear …
This is the first monograph on codebooks and linear codes from difference sets and almost difference sets. It aims at providing a survey of constructions of difference sets and almost difference sets as well as an in-depth treatment of codebooks and linear codes from difference …