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Asymptotic Lower Bound for Quasi Transitive Codes over Cubic Finite Fields

Electronic Theses of Indian Institute of Science

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Title Asymptotic Lower Bound for Quasi Transitive Codes over Cubic Finite Fields
 
Creator Ethamakula, Bharath Kumar
 
Subject Algebraic Geometry
Quasi-Transitive Codes
Cubic Finite Field
Bassa-Garcia-Stichtenoth Tower
BGS Tower
Quasi Transitive Codes
G28196
 
Description Algebraic geometric codes were first introduced by V.D.Goppa . They were well recognized and developed by Tsfasman, Vladut and Zink because they have parameters better than Gilbert-Varshmov bound and thus giving rise to Tsfasman Vladut-Zink bound. While the codes given by Ihara, Tsfasman, Vladut and Zink have complicated construction, Garcia and Stichtenoth on the other hand gave an explicit construction of codes attaining Tsfasman-Vlasut-Zink bound using the terminology of function fields. In coding theory one of the challenging problem is to find a sequence of cyclic codes that are asymptotically good. While this has not been achieved, Stichtenoth generalized cyclic codes to transitive codes and constructed a sequence of asymptotically good transitive codes on algebraic function fields over quadratic finite fields that attain Tsfasman-Vladut-Zink bound.
In the case of cubic finite fields, Bezerra, Garcia and Stichtenoth constructed a tower of function fields over cubic finite fields whose limit attains a lower bound and the codes constructed over this tower turns out to be asymptotically good attaining a positive lower bound. Bassa used this tower and constructed quasi transitive codes which are a generalization of transitive codes and proved that they are also asymptotically good and attain the same positive lower bound. Later Bassa, Garcia and Stichtenoth constructed a new tower of function fields over cubic finite fields whose structure is less complicated compared to that of Bezerra, Garcia and Stichtenoths' and proved that codes constructed over it also attain the same positive lower bound. In this work along the lines of Bassa and Stichtenoth we construct quasi transitive codes over the tower given by Bassa, Garcia and Stichtenoth and prove that these quasi transitive codes are also asymptotically good and also attain the same lower bound.
 
Contributor Patil, D P
Vijay Kumar, P
 
Date 2018-07-14T06:45:02Z
2018-07-14T06:45:02Z
2018-07-14
2015
 
Type Thesis
 
Identifier http://etd.iisc.ernet.in/2005/3821
http://etd.iisc.ernet.in/abstracts/4692/G28196-Abs.pdf
 
Language en_US
 
Relation G28196