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Please use this identifier to cite or link to this item: http://dspace.library.iitb.ac.in/jspui/handle/10054/3390

Title: Schubert varieties, linear codes and enumerative combinatorics
Authors: GHORPADE, SR
TSFASMAN, MA
Issue Date: 2005
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Citation: FINITE FIELDS AND THEIR APPLICATIONS, 11(4), 684-699
Abstract: 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
URI: 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
ISSN: 1071-5797
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