Additive codes and their geometric counterparts

Title data

Kurz, Sascha:
Additive codes and their geometric counterparts.
2026
Event: Galois geometries and their applications , 12.02.2026 , Neapel, Italien (online).
(Conference item: Lecture series , Speech )

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Abstract in another language

Geometrically additive codes correspond to multisets of subspaces in a projective space. The minmum distance corresponds to the maximum number of elements contained in a hyperplane. If the replace hyperplane by codimension f subspaces, then the coding equivalent is the generalized f-th Hamming weight of an additive (or linear) code. This opens a large geometric playground. In the talk we give a few constructions and upper bounds for the maximum number n_q(r,h,f;s) of h-spaces in PG(r-1,q) such that at most s elements are contained in each codimension f subspace.