<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></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.

Projective parameterized linear codes

Departamento de Ciencias Básicas, Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, Instituto Politécnico Nacional, 07340,

Departamento de Matemáticas, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, 07300,

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Projective parameterized linear codes"}

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...

Projective parameterized linear codes

Published Online: Apr 22, 2017

Page range: 223 - 240

Received: Feb 01, 2013

Accepted: Oct 01, 2013

DOI: https://doi.org/10.1515/auom-2015-0039

Keywords
Parameterized code, projective space, minimum distance, regularity index

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Projective parameterized linear codes

Published Online: Apr 22, 2017

Page range: 223 - 240

Received: Feb 01, 2013

Accepted: Oct 01, 2013

DOI: https://doi.org/10.1515/auom-2015-0039

KeywordsParameterized code, projective space, minimum distance, regularity index

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Parameterized code, projective space, minimum distance, regularity index