Classical Varieties, Codes and Combinatorics
Classical Varieties, Codes and Combinatorics
Sudhir R. Ghorpade
1
Department of Mathematics
Indian Institute of Technology Bombay,
Powai, Mumbai 400076, India
E-Mail: srg@math.iitb.ac.in
and
Michael A. Tsfasman
2
Institut de Mathématiques de Luminy,
Case 907, 13288 Marseille, France
and
Independent University of Moscow
and
Dorbushin Math. Lab., Institute for Information Transmission Problems, Moscow
E-Mail: tsfasman@iml.univ-mrs.fr
Abstract
This article is an extended abstract of the paper
Schubert varieties, linear codes and
enumerative combinatorics, and attempts to
provide a motivated and leisurely introduction
to the latter. A brief outline of some related developments is also included.
Contents
1 | Introduction | 1 |
2 | Linear Codes and Projective Systems | 1 |
3 | Grassmann Codes and Schubert Codes | 2 |
4 | Length of Schubert Codes | 4 |
5 | Dimension of Schubert Codes | 6 |
6 | Minimum Distance Conjecture for Schubert Divisors | 8 |
7 | Related Developments | 8 |
| References | 9 |
1
Partially supported by the IRCC grant 97IR012 from IIT Bombay.
2
Partially supported by the RFBR grants 99-01-01204, 02-01-01041 and 02-01-22005.
This article appears in:
Formal Power Series and Algebraic
Combinatorics, (Vadstena, 2003) Actes/Proceedings,
K. Eriksson and S. Linusson Eds., Linköping University,
Sweden (2003), pp. 75-84.
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