Linear sets on the projective line have attracted a lot of attention because of their link with blocking sets, KM-arcs and rank-metric codes. In this paper, we study linear sets having two points of complementary weight, that is, with two points for which the sum of their weights equals the rank of the linear set. As a special case, we study those linear sets having exactly two points of weight greater than one, by showing new examples and studying their equivalence issue. Also, we determine some linearized polynomials defining the linear sets recently introduced by Jena and Van de Voorde [30].
Linear sets on the projective line with complementary weights
Napolitano V.;Polverino O.
;Santonastaso P.;Zullo F.
2022
Abstract
Linear sets on the projective line have attracted a lot of attention because of their link with blocking sets, KM-arcs and rank-metric codes. In this paper, we study linear sets having two points of complementary weight, that is, with two points for which the sum of their weights equals the rank of the linear set. As a special case, we study those linear sets having exactly two points of weight greater than one, by showing new examples and studying their equivalence issue. Also, we determine some linearized polynomials defining the linear sets recently introduced by Jena and Van de Voorde [30].File in questo prodotto:
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