Vector Space Partitions


Topic:Vector Space Partitions

Speaker: Professor George F. Seelinger

Event date: 6/3/2019

Event time: 16:30 p.m.

Venue: Lecture Hall1506, Building 9

Sponsor: School of Mathematics and Statics, Institute of Science and Technology


Let F be a field and letV be a finite-dimensional F-vector space. We say P is a vector space partitionof V if P is a collection of nonzero subspaces of V such that (1) ∪ U∈PU = V and (2) if U andU´ aredistinct subspaces of V, then U ∩ U´ = {0}. When F is a finite field, this gives a way toconstruct error-correcting codes. The main question is to classify all suchvector space partitions for a given vector space V. In this talk, we willconsider the case when F is a finite field of characteristic 2 and discussvarious constructions of such partitions. We will also introduce multi-foldpartitions and state some interesting questions in this context.