$δ$-sequences and Evaluation Codes defined by Plane Valuations at Infinity
| dc.creator | Galindo, C. | |
| dc.creator | Monserrat, F. | |
| dc.date | 2007-04-26 | |
| dc.date | 2008-07-14 | |
| dc.date.accessioned | 2026-07-07T09:49:44Z | |
| dc.date.available | 2026-07-07T09:49:44Z | |
| dc.description | We introduce the concept of $δ$-sequence. A $δ$-sequence $Δ$ 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 $Δ$ 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. | |
| dc.identifier | https://arxiv.org/abs/0704.3536 | |
| dc.identifier | http://arxiv.org/abs/0704.3536 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164699 | |
| dc.subject | Information Theory | |
| dc.title | $δ$-sequences and Evaluation Codes defined by Plane Valuations at Infinity | |
| dc.type | text |