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 \(\mathbb {P}^n(\mathbb {F}_q)\), 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.
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The Cícero Carvalho and V. G. Lopez Neumann are partially supported by CNPq and by FAPEMIG. The Hiram H. López was partially supported by CONACyT and Universidad Autónoma de Aguascalientes.
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Carvalho, C., Neumann, V.G.L. & López, H.H. Projective Nested Cartesian Codes. Bull Braz Math Soc, New Series 48, 283–302 (2017). https://doi.org/10.1007/s00574-016-0010-z
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DOI: https://doi.org/10.1007/s00574-016-0010-z