Projective nested cartesian codes

Fuente: arXiv
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Main Authors: Carvalho, Cicero, Neumann, V. G. Lopez, Lopez, Hiram H.
Format: Preprint
Published: 2014
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author Carvalho, Cicero
Neumann, V. G. Lopez
Lopez, Hiram H.
author_facet Carvalho, Cicero
Neumann, V. G. Lopez
Lopez, Hiram H.
contents In this paper we introduce a new type of code, called projective nested cartesian code. It is obtained by the evaluation of homogeneous polynomials of a fixed degree on a certain subset of $\mathbb{P}^n(\mathbb{F}_q)$, and they may be seen as a generalization of the so-called projective Reed-Muller codes. We calculate the length and the dimension of such codes, a lower bound for the minimum distance and the exact minimum distance in a special case (which includes the projective Reed-Muller codes). At the end we show some relations between the parameters of these codes and those of the affine cartesian codes.
format Preprint
id arxiv_https___arxiv_org_abs_1411_6819
institution arXiv
publishDate 2014
record_format arxiv
spellingShingle Projective nested cartesian codes
Carvalho, Cicero
Neumann, V. G. Lopez
Lopez, Hiram H.
Algebraic Geometry
Number Theory
14G50 (Primary), 11T71 (Secondary)
In this paper we introduce a new type of code, called projective nested cartesian code. It is obtained by the evaluation of homogeneous polynomials of a fixed degree on a certain subset of $\mathbb{P}^n(\mathbb{F}_q)$, and they may be seen as a generalization of the so-called projective Reed-Muller codes. We calculate the length and the dimension of such codes, a lower bound for the minimum distance and the exact minimum distance in a special case (which includes the projective Reed-Muller codes). At the end we show some relations between the parameters of these codes and those of the affine cartesian codes.
title Projective nested cartesian codes
topic Algebraic Geometry
Number Theory
14G50 (Primary), 11T71 (Secondary)
url https://arxiv.org/abs/1411.6819