Projective Parameterized Linear Codes Arising from some Matrices and their Main Parameters
In this paper we will estimate the main parameters of some evaluation codes which are known as projective parameterized codes. We will find the length of these codes and we will give a formula for the dimension in terms of the Hilbert function associated to two ideals, one of them being the vanishin...
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| Main Authors | , , |
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| Format | Journal Article |
| Language | English |
| Published |
30.08.2011
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| Subjects | |
| Online Access | Get full text |
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| Abstract | In this paper we will estimate the main parameters of some evaluation codes
which are known as projective parameterized codes. We will find the length of
these codes and we will 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 will find an upper bound for the minimum
distance and, in some cases, we will 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. |
|---|---|
| AbstractList | In this paper we will estimate the main parameters of some evaluation codes
which are known as projective parameterized codes. We will find the length of
these codes and we will 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 will find an upper bound for the minimum
distance and, in some cases, we will 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. |
| Author | Sarabia, Manuel Gonzalez Marquez, Carlos Renteria Rosales, Eliseo Sarmiento |
| Author_xml | – sequence: 1 givenname: Manuel Gonzalez surname: Sarabia fullname: Sarabia, Manuel Gonzalez – sequence: 2 givenname: Carlos Renteria surname: Marquez fullname: Marquez, Carlos Renteria – sequence: 3 givenname: Eliseo Sarmiento surname: Rosales fullname: Rosales, Eliseo Sarmiento |
| BackLink | https://doi.org/10.48550/arXiv.1108.6114$$DView paper in arXiv |
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| Snippet | In this paper we will estimate the main parameters of some evaluation codes
which are known as projective parameterized codes. We will find the length of
these... |
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| SourceType | Open Access Repository |
| SubjectTerms | Computer Science - Information Theory Mathematics - Information Theory |
| Title | Projective Parameterized Linear Codes Arising from some Matrices and their Main Parameters |
| URI | https://arxiv.org/abs/1108.6114 |
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