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Weight Spectrum of Codes Associated With the Grassmannian G(3,7)

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Title Weight Spectrum of Codes Associated With the Grassmannian G(3,7)
 
Creator KAIPA, KV
PILLAI, HK
 
Subject Grassmannian
Pfaffian
trilinear alternating forms
weight spectrum
 
Description In this paper, we consider the problem of determining the weight spectrum of q-ary codes C(3, m) associated with Grassmann varieties G(3, m) For, m = 6, this was done in a paper by Nogin in 1997. We derive a formula for the weight of a codeword of C(3, m), in terms of certain varieties associated with alternating trilinear forms on F-q(m). The classification of such forms under the action of the general linear group GL(m, F-q) is the other component that is required to calculate the spectrum of C(3, m). For, m = 7, we explicitly determine the varieties mentioned above. The classification problem for alternating three-forms on F-q(7) was solved in a study by Cohen and Helminck in 1988, which we then use to determine the spectrum of C(3, 7).
 
Publisher IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
 
Date 2014-10-16T07:12:13Z
2014-10-16T07:12:13Z
2013
 
Type Article
 
Identifier IEEE TRANSACTIONS ON INFORMATION THEORY, 59(2)986-993
http://dx.doi.org/10.1109/TIT.2012.2219497
http://dspace.library.iitb.ac.in/jspui/handle/100/15521
 
Language en