Affine Grassmann Codes
Affine Grassmann Codes
Peter Beelen
Department of Mathematics,
Technical University of Denmark,
DK 2800, Lyngby, Denmark
E-Mail: p.beelen@mat.dtu.dk
Sudhir R. Ghorpade
Department of Mathematics
Indian Institute of Technology Bombay
Powai, Mumbai 400076, India
E-Mail: srg@math.iitb.ac.in
and
Tom Høholdt
Department of Mathematics,
Technical University of Denmark,
DK 2800, Lyngby, Denmark
E-Mail: T.Hoeholdt@mat.dtu.dk
Abstract
We consider a new class of linear codes, called affine
Grassmann codes. These can be viewed as a variant of generalized
Reed-Muller codes and are closely related to Grassmann codes.We
determine the length, dimension, and the minimum distance of any
affine Grassmann code. Moreover, we show that affine Grassmann
codes have a large automorphism group and determine the number
of minimum weight codewords.
| 1 | Introduction | 1 |
| 2 | Preliminaries | 1 |
| 3 | Minimum Distance | 5 |
| 4 | Automorphisms | 9 |
| 5 | Characterization of Minimum Weight Codewords | 10 |
| 6 | Enumeration of Minimum Weight Codewords | 13 |
| 7 | Connection with Grassmann Codes | 15 |
| References | 17 |
This paper is published in the IEEE Transactions on Information Theory,
Vol. 56, No. 7 (2010), 3166-3176.
[Preprint Version: arXiv.math/0911.1298v2 (June 2010)]
Download the full paper as:
Back to the List of Publications
Back to the Sudhir Ghorpade's Home Page