  We introduce the concept of $\delta$-sequence. A $\delta$-sequence $\Delta$
generates a well-ordered semigroup $S$ in $\mathbb{Z}^2$ or $\mathbb{R}$. We
show how to construct (and compute parameters) for the dual code of any
evaluation code associated with a weight function defined by $\Delta$ 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 $\delta$-sequences of the different existing types, and so this paper
provides the tools to know and use a new large set of codes.
