4 papers
Attaining Capacity with Algebraic Geometry Codes through the Construction and Koetter-Vardy Soft Decoding
Irene Marquez-Corbella, Jean-Pierre Tillich
In this paper we show how to attain the capacity of discrete symmetric channels with polynomial time decoding complexity by considering iterated constructions with Reed-S…
A characterization of MDS codes that have an error correcting pair
Irene Márquez-Corbella, Ruud Pellikaan
Error-correcting pairs were introduced in 1988 by R. Pellikaan, and were found independently by R. Kötter (1992), as a general algebraic method of decoding linear codes. These pair…
On the Composition of Secret Sharing Schemes Related to Codes
Irene Márquez-Corbella, Edgar Martínez-Moro, Emilio Suárez-Canedo
In this paper we construct a subclass of the composite access structure introduced by Martínez et al. based on schemes realizing the structure given by the set of codewords of mini…
On the ideal associated to a linear code
Irene Márquez-Corbella, Edgar Martínez-Moro, Emilio Suárez-Canedo
This article aims to explore the bridge between the algebraic structure of a linear code and the complete decoding process. To this end, we associate a specific binomial ideal $I_+…