Discrete Equivalence of Non-positive at Infinity Plane Valuations

Evaluation codes defined by finite families of plane valuations at infinity

We construct evaluation codes given by weight functions defined over polynomial rings in m ≥ 2 indeterminates. These weight functions are determined by sets of m− 1 weight functions over polynomial rings in two indeterminates defined by plane valuations at infinity. Well-suited families in totally ordered commutative groups are an important tool in our procedure.

Evaluation Codes Defined by Plane Valuations at Infinity C. Galindo and F. Monserrat

We introduce the concept of δ-sequence. A δ-sequence ∆ generates a wellordered semigroup S in Z 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 p...

Δ-sequences and Evaluation Codes Defined by Plane Valuations at Infinity

We introduce the concept of δ-sequence. A δ-sequence ∆ generates a well-ordered semigroup S in Z 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 ...

$\delta$-sequences and Evaluation Codes defined by Plane Valuations at Infinity

We introduce the concept of δ-sequence. A δ-sequence ∆ generates a well-ordered semigroup S in Z 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 ...

Construction of Affine Plane Curves with One Place at Infinity