Projective nested cartesian codes
Algebraic Geometry
2024-02-07 v2 Number Theory
Abstract
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 , 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.
Cite
@article{arxiv.1411.6819,
title = {Projective nested cartesian codes},
author = {Cicero Carvalho and V. G. Lopez Neumann and Hiram H. Lopez},
journal= {arXiv preprint arXiv:1411.6819},
year = {2024}
}