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Decomposable subspaces, linear sections of Grassmann varieties, and higher weights of Grassmann codes

DSpace at IIT Bombay

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Title Decomposable subspaces, linear sections of Grassmann varieties, and higher weights of Grassmann codes
 
Creator GHORPADE, SR
PATIL, AR
PILLAI, HK
 
Subject exterior algebra
decomposable subspace
grassmann variety
linear code
higher weight
griesmer-wei bound
grassmann code
 
Description We consider the question of determining the maximum number of points on sections of Grassmannians over finite fields by linear subvarieties of the Plucker projective space of a fixed codimension. This corresponds to a known open problem of determining the complete weight hierarchy of linear error correcting codes associated to Grassmann varieties. We recover most of the known results as well as prove some new results. A basic tool used is a characterization of decomposable subspaces of exterior powers, that is, subspaces in which every nonzero element is decomposable. Also. we use a generalization of the Griesmer-Wei bound that is proved here for arbitrary linear codes. (C) 2008
 
Publisher ACADEMIC PRESS INC ELSEVIER SCIENCE
 
Date 2011-07-12T14:45:33Z
2011-12-26T12:48:56Z
2011-12-27T05:34:28Z
2011-07-12T14:45:33Z
2011-12-26T12:48:56Z
2011-12-27T05:34:28Z
2009
 
Type Article
 
Identifier FINITE FIELDS AND THEIR APPLICATIONS, 15(1), 54-68
1071-5797
http://dx.doi.org/10.1016/j.ffa.2008.08.001
http://dspace.library.iitb.ac.in/xmlui/handle/10054/3356
http://hdl.handle.net/10054/3356
 
Language en