Near Orders and Codes

Høholdt, van Lint, and Pellikaan used order functions to construct codes by means of Linear Algebra and Semigroup Theory only. However, Geometric Goppa codes that can be represented by this method are mainly those based on just one point. In this correspondence, we introduce the concept of near order function with the aim of generalizing this approach in such a way that a wider family of Geometric Goppa codes can be studied on a more elementary setting.