(Multi-)Sets of subspaces and divisible codes

Title data

Heinlein, Daniel ; Honold, Thomas ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
(Multi-)Sets of subspaces and divisible codes.
2018
Event: Algebraic Coding Theory for Networks, Storage, and Security , 16-21.12.2018 , Schloß Dagstuhl, Wadern.
(Conference item: Workshop , Speech )

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Abstract in another language

A multi set of subspaces in GF(q)^v gives rise to a q^r divisible linear code if the dimensions of the subspaces are at least r+1. This connection has implications e.g. for the existence of vector space partitions, packing or covering problems for subspaces, or subspace codes. Several optimal linear codes in the Hamming metric are divisible. The cylinder conjecture of Ball is actually a classification statement for divisible codes. Extendability results for partial spreads concluded from minihypers can be obtained via divisible codes. Generalizations also permit extendability results for codes in the rank metric or subspace codes.
The aim of this talk is to give a brief introduction to the connection between multisets of subspaces and divisible codes, survey some results and applications of q^r divisible codes, and, most importantly, to encourage collaboration from other participants.