Two pointsets in PG(2,q^n) and the associated codes

12/22/2021

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by   Vito Napolitano, et al.

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Università degli Studi della Campania "Luigi Vanvitelli"

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In this paper we consider two pointsets in PG(2,q^n) arising from a linear set L of rank n contained in a line of PG(2,q^n): the first one is a linear blocking set of Rédei type, the second one extends the construction of translation KM-arcs. We point out that their intersections pattern with lines is related to the weight distribution of the considered linear set L. We then consider the Hamming metric codes associated with both these constructions, for which we can completely describe their weight distributions. By choosing L to be an 𝔽_q-linear set with a short weight distribution, then the associated codes have few weights. We conclude the paper by providing a connection between the ΓL-class of L and the number of inequivalent codes we can construct starting from it.