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Projective Nested Cartesian Codes

Projective Nested Cartesian Codes In this paper we introduce a new family of codes, called projective nested cartesian codes. They are obtained by the evaluation of homogeneous polynomials of a fixed degree on a certain subset of $$\mathbb {P}^n(\mathbb {F}_q)$$ P n ( 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, an upper 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

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References (14)

Publisher
Springer Journals
Copyright
Copyright © 2016 by Sociedade Brasileira de Matemática
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s00574-016-0010-z
Publisher site
See Article on Publisher Site

Abstract

In this paper we introduce a new family of codes, called projective nested cartesian codes. They are obtained by the evaluation of homogeneous polynomials of a fixed degree on a certain subset of $$\mathbb {P}^n(\mathbb {F}_q)$$ P n ( 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, an upper 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.

Journal

Bulletin of the Brazilian Mathematical Society, New SeriesSpringer Journals

Published: Oct 5, 2016

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