Abstract
In 1988 Lachaud introduced the class of projective Reed–Muller codes, defined by evaluating the space of homogeneous polynomials of a fixed degree d on the points of $$\mathbb {P}^n(\mathbb {F}_q)$$ . In this paper we evaluate the same space of polynomials on the points of a higher dimensional scroll, defined from a set of rational normal curves contained in complementary linear subspaces of a projective space. We determine a formula for the dimension of the codes, and the exact value of the dimension and the minimum distance in some special cases.
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