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Projective parameterized linear codes Cover

Abstract

In this paper we estimate the main parameters of some evaluation codes which are known as projective parameterized codes. We find the length of these codes and we give a formula for the dimension in terms of the Hilbert function associated to two ideals, one of them being the vanishing ideal of the projective torus. Also we find an upper bound for the minimum distance and, in some cases, we give some lower bounds for the regularity index and the minimum distance. These lower bounds work in several cases, particularly for any projective parameterized code associated to the incidence matrix of uniform clutters and then they work in the case of graphs.

DOI: https://doi.org/10.1515/auom-2015-0039 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 223 - 240
Submitted on: Feb 1, 2013
Accepted on: Oct 1, 2013
Published on: Apr 22, 2017
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2017 Manuel González Sarabia, Carlos Rentería Márquez, Eliseo Sarmiento Rosales, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.