Generalized vector space partitions
Daniel Heinlein, Thomas Honold, Michael Kiermaier, Sascha Kurz

TL;DR
This paper generalizes the concept of vector space partitions to include t-dimensional subspaces, exploring their properties and connections to subspace codes, with some problems remaining open even in the simplified case.
Contribution
It introduces the notion of vector space t-partitions, extending classical partitions and analyzing their properties and relationships to subspace coding theory.
Findings
Established properties of vector space t-partitions
Connected t-partitions to subspace codes
Identified open problems for q=1 case
Abstract
A vector space partition in is a set of subspaces such that every -dimensional subspace of is contained in exactly one element of . Replacing "every point" by "every -dimensional subspace", we generalize this notion to vector space -partitions and study their properties. There is a close connection to subspace codes and some problems are even interesting and unsolved for the set case .
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cooperative Communication and Network Coding
