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



Michael A. Tsfasman 2

Institut de Mathématiques de Luminy, Case 907, 13288 Marseille, France
Independent University of Moscow
Dorbushin Math. Lab., Institute for Information Transmission Problems, Moscow


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.


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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