We present characterizations of extractors and Kolmogorov extractors in terms of a combinatorial object called balanced table. These characterizations provide an alternative proof for the relation between extractors and Kolmogorov extractors, first obtained in [FHP06] and [HPV09].

The notion of Kolmogorov complexity (=the minimal length of a program that generates some object) is often useful as a kind of language that allows us to reformulate some notions and therefore provide new intuition. In this survey we provide (with minimal comments) many different examples where notions and statements that involve Kolmogorov complexity are compared with their counterparts not in...

We present families of unital algebras obtained through a doubling process from a cyclic central simple algebra D = (K/F, σ, c), employing a K-automorphism τ and an element d ∈ D×. These algebras appear in the construction of iterated spacetime block codes. We give conditions when these iterated algebras are division which can be used to construct fully diverse iterated codes. We also briefly l...