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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.
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Oct 5, 2016
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