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Linear sets in coding theory

Coding Theory and Cryptography Seminars

Linear sets are a natural generalization of projective subspaces and of subgeometries in a projective space over a finite field. They were introduced by Lunardon in 1999 to construct some examples of blocking sets, which are now known as linear blocking sets. In recent years, they have been intensively used to construct, to classify and to characterize many different geometrical and algebraic objects like two-intersection sets, complete caps, translation spreads of the Cayley Generalized Hexagon, translation ovoids of polar spaces, semifield flocks, finite semifields and linear codes. In this talk we will explore how the geometry of linear sets can give constructions and classification results in coding theory.