Enumeration of Splitting Subspaces over Finite Fields
Enumeration of Splitting Subspaces over Finite Fields
Sudhir R. Ghorpade
Department of Mathematics
Indian Institute of Technology Bombay
Powai, Mumbai 400076, India
E-Mail: srg@math.iitb.ac.in
and
Samrith Ram
Department of Mathematics
Indian Institute of Technology Bombay
Powai, Mumbai 400076, India
E-Mail: samrith@gmail.com
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.
| 1 | Introduction | 1 |
| 2 | Easy cases and guesse | 2 |
| 3 | Splitting planes | 3 |
| 4 | Refinements and Extensions | 5 |
| A |
Appendix: Vector Recurrences and Singer Cycles | 8 |
| References | 10 |
This paper is published in:
Arithmetic, Geometry, Cryptography and Coding Theory,
(Luminy, France, March 2011
),
Y. Aubry, C. Ritzenthaler, and A. Zykin Eds.,
Contemporary Mathematics, Vol. 574,
American Mathematical Society, Providence, RI, 2012, pp. 49-58.
[Preprint Version:
arXiv.math/1203.1849 (Mar 2012)]
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