δ-sequences and evaluation codes defined by plane valuations at infinity
Carlos Galindo, Francisco Monserrat · Proceedings of the London Mathematical Society · 2008
Abstract. We introduce the concept of δ-sequence. A δ-sequence ∆ generates a well-ordered semigroup S in Z 2 or R. We show how to construct (and compute parameters) for the dual code of any evaluation code associated with a weight function defined by ∆ from the polynomial ring in two indeterminates to a semigroup S as above. We prove that this is a simple procedure which can be understood by considering a particular class of valuations of function fields of surfaces, called plane valuations at infinity. We also give algorithms to construct an unlimited number of δ-sequences of the different existing types, and so this paper provides the tools to know and use a new large set of codes. 1.