Enumeration of Splitting Subspaces over Finite Fields
Sudhir R. Ghorpade, Samrith Ram
TL;DR
This paper explores an unsolved problem in finite field theory related to counting specific subspaces, providing recent progress and discussing related open problems in the area.
Contribution
It offers a concise overview of recent advances in enumerating splitting subspaces over finite fields and discusses related unresolved problems.
Findings
Recent progress on counting splitting subspaces
Discussion of related open problems in finite field theory
Elementary approach to a complex enumeration problem
Abstract
We discuss an elementary, yet unsolved, problem of Niederreiter concerning the enumeration of a class of subspaces of finite dimensional vector spaces over finite fields. A short and self-contained account of some recent progress on this problem is included and some related problems are discussed.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Finite Group Theory Research