Strong (t mod q)-arcs in PG(k-1,q)

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Kurz, Sascha ; Landjev, Ivan ; Rousseva, Assia:
Strong (t mod q)-arcs in PG(k-1,q).
2022
Veranstaltung: Finite Geometries 2022 - Sixth Irsee Conference , 28.08.-03.09.2022 , Irsee, Deutschland.
(Veranstaltungsbeitrag: Workshop , Vortrag )

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Abstract

Several extendability results for linear codes can be explained geometrically using the structure of so-called (strong) (t mod q) arcs in PG(k − 1, q). In this talk we provide a new classification theorem for strong (3 mod 5) arcs in PG(3, 5), where three examples disprove a conjecture of Landjev and Rousseva. The classification is used to show the non-existence of a [104, 4, 82]_5 code.