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Subclose families, threshold graphs, and the weight hierarchy of Grassmann and Schubert Codes

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Title Subclose families, threshold graphs, and the weight hierarchy of Grassmann and Schubert Codes
 
Creator GHORPADE, SR
PATIL, AR
PILLAI, HK
 
Subject linear codes
varieties
squares
sum
linear code
higher weight
grassmann variety
grassmann code
schubert variety
schubert code
threshold graph
optimal graph
 
Description We discuss the problem of determining the complete weight hierarchy of linear error correcting codes associated to Grassmann varieties and. more generally, to Schubert varieties in Grassmannians. In geometric terms, this corresponds to the determination of the maximum number of F.-rational points on sections of Schubert varieties (with nondegenerate Plucker embedding) by linear subvarieties of a fixed (co)dimension. The problem is partially solved in the case of Grassmann codes, and one of the solutions uses the combinatorial notion of a close family. We propose a generalization of this to what is called a subclose family. A number of properties of subclose families are proved, and its connection with the notion of threshold graphs and graphs with maximum sum of squares of vertex degrees is outlined.
 
Publisher AMER MATHEMATICAL SOC
 
Date 2011-10-23T07:42:15Z
2011-12-15T09:11:03Z
2011-10-23T07:42:15Z
2011-12-15T09:11:03Z
2009
 
Type Proceedings Paper
 
Identifier ARITHMETIC, GEOMETRY, CRYPTOGRAPHY AND CODING THEORY,487,87-99
978-0-8218-4716-9
0271-4132
http://dspace.library.iitb.ac.in/xmlui/handle/10054/15068
http://hdl.handle.net/100/1819
 
Source 11th Conference on Arithmetic, Geometry, Cryptography and Coding Theory,Marseilles, FRANCE,NOV 05-09, 2007
 
Language English