De Bruijn cycles and their application for encoding of discrete positions
We explore the borderline between decidability and undecidability of the following question: “Let C be a class of codes. Given a machine of type X, is it decidable whether the language lies in C or not?” for codes in general, ω-codes, codes of finite and bounded deciphering delay, prefix, suffix and bi(pre)fix codes, and for finite automata equipped with different versions of push-down stores and counters.
The purpose of the present article is the study of duals of functional codes on algebraic surfaces. We give a direct geometrical description of them, using differentials. Even if this description is less trivial, it can be regarded as a natural extension to surfaces of the result asserting that the dual of a functional code on a curve is the differential code . We study the parameters of such codes and state a lower bound for their minimum distance. Using this bound, one can study some examples...
This paper surveys parts of the study of divisibility properties of codes. The survey begins with the motivating background involving polynomials over finite fields. Then it presents recent results on bounds and applications to optimal codes.