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Linear codes associated to determinantal varieties

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Title Linear codes associated to determinantal varieties
 
Creator BEELEN, P
GHORPADE, SR
UL HASAN, S
 
Subject HIGHER WEIGHTS
Linear codes
Determinantal varieties
Generalized Hamming weight
Weight distribution
 
Description We consider a class of linear codes associated to projective algebraic varieties defined by the vanishing of minors of a fixed size of a generic matrix. It is seen that the resulting code has only a small number of distinct weights. The case of varieties defined by the vanishing of 2 x 2 minors is considered in some detail. Here we obtain the complete weight distribution. Moreover, several generalized Hamming weights are determined explicitly and it is shown that the first few of them coincide with the distinct nonzero weights. One of the tools used is to determine the maximum possible number of matrices of rank 1 in a linear space of matrices of a given dimension over a finite field. In particular, we determine the structure and the maximum possible dimension of linear spaces of matrices in which every nonzero matrix has rank 1. (C) 2015 Elsevier B.V. All rights reserved.
 
Publisher ELSEVIER SCIENCE BV
 
Date 2016-01-14T13:37:27Z
2016-01-14T13:37:27Z
2015
 
Type Article
 
Identifier DISCRETE MATHEMATICS, 338(8)1493-1500
0012-365X
1872-681X
http://dx.doi.org/10.1016/j.disc.2015.03.009
http://dspace.library.iitb.ac.in/jspui/handle/100/17633
 
Language en