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Automorphism groups of Grassmann codes

DSpace at IIT Bombay

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Field Value
 
Title Automorphism groups of Grassmann codes
 
Creator GHORPADE, SR
KAIPA, KV
 
Subject Grassmann variety
Schubert divisor
Linear code
Automorphism group
Grassmann code
Affine Grassmann code
EQUIVALENCE
SPACES
 
Description We use a theorem of Chow (1949) on line-preserving bijections of Grassmannians to determine the automorphism group of Grassmann codes. Further, we analyze the automorphisms of the big cell of a Grassmannian and then use it to settle an open question of Beelen et al. (2010) concerning the permutation automorphism groups of affine Grassmann codes. Finally, we prove an analogue of Chow's theorem for the case of Schubert divisors in Grassmannians and then use it to determine the automorphism group of linear codes associated to such Schubert divisors. In the course of this work, we also give an alternative short proof of MacWilliams theorem concerning the equivalence of linear codes and a characterization of maximal linear subspaces of Schubert divisors in Grassmannians. (c) 2013 Elsevier Inc. All rights reserved.
 
Publisher ACADEMIC PRESS INC ELSEVIER SCIENCE
 
Date 2014-10-16T13:42:06Z
2014-10-16T13:42:06Z
2013
 
Type Article
 
Identifier FINITE FIELDS AND THEIR APPLICATIONS, 2380-102
1071-5797
1090-2465
http://dx.doi.org/10.1016/j.ffa.2013.04.005
http://dspace.library.iitb.ac.in/jspui/handle/100/15693
 
Language en