Record Details

Schubert varieties, linear codes and enumerative combinatorics

DSpace at IIT Bombay

View Archive Info
 
 
Field Value
 
Title Schubert varieties, linear codes and enumerative combinatorics
 
Creator GHORPADE, SR
TSFASMAN, MA
 
Subject grassmannian
linear codes
minimum distance
projective system
schubert variety
 
Description We consider linear error correcting codes associated to higher-dimensional projective varieties defined over a finite field. The problem of determining the basic parameters of such codes often leads to some interesting and difficult questions in combinatorics and algebraic geometry. This is illustrated by codes associated to Schubert varieties in Grassmannians, called Schubert codes, which have recently been studied. The basic parameters such as the length, dimension and minimum distance of these codes are known only in special cases. An upper bound for the minimum distance is known and it is conjectured that this bound is achieved. We give explicit formulae for the length and dimension of arbitrary Schubert codes and prove the minimum distance conjecture in the affirmative for codes associated to Schubert divisors. (c) 2004
 
Publisher ACADEMIC PRESS INC ELSEVIER SCIENCE
 
Date 2011-07-12T17:01:47Z
2011-12-26T12:48:59Z
2011-12-27T05:34:33Z
2011-07-12T17:01:47Z
2011-12-26T12:48:59Z
2011-12-27T05:34:33Z
2005
 
Type Article
 
Identifier FINITE FIELDS AND THEIR APPLICATIONS, 11(4), 684-699
1071-5797
http://dx.doi.org/10.1016/j.ffa.2004.09.002
http://dspace.library.iitb.ac.in/xmlui/handle/10054/3390
http://hdl.handle.net/10054/3390
 
Language en