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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