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Advances in Mathematics of Communications (AMC)
 

Self-dual [62, 31, 12] and [64, 32, 12] codes with an automorphism of order 7

Pages: 73 - 81, Volume 8, Issue 1, February 2014      doi:10.3934/amc.2014.8.73

 
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Nikolay Yankov - Faculty of Mathematics and Informatics, Konstantin Preslavski University of Shumen, Shumen, 9712, Bulgaria (email)

Abstract: This paper studies and classifies all binary self-dual $[62, 31, 12]$ and $[64, 32, 12]$ codes having an automorphism of order 7 with 8 cycles. This classification is done by applying a method for constructing binary self-dual codes with an automorphism of odd prime order $p$. There are exactly 8 inequivalent binary self-dual $[62, 31, 12]$ codes with an automorphism of type $7-(8,6)$. As for binary $[64,32,12]$ self-dual codes with an automorphism of type $7-(8,8)$ there are 44465 doubly-even and 557 singly-even such codes. Some of the constructed singly-even codes for both lengths have weight enumerators for which the existence was not known before.

Keywords:  Automorphisms, self-dual codes.
Mathematics Subject Classification:  Primary: 11T71; Secondary: 94B05.

Received: February 2013;      Revised: June 2013;      Available Online: January 2014.

 References