Projective nested cartesian codes
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arXiv
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| Format: | Preprint |
| Published: |
2014
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| _version_ | 1866929234759385088 |
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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 |