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Classification of ternary extremal self-dual codes of length 28


Authors: Masaaki Harada, Akihiro Munemasa and Boris Venkov
Journal: Math. Comp. 78 (2009), 1787-1796
MSC (2000): Primary 94B05; Secondary 11H71
DOI: https://doi.org/10.1090/S0025-5718-08-02194-7
Published electronically: October 24, 2008
MathSciNet review: 2501075
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Abstract: All $ 28$-dimensional unimodular lattices with minimum norm $ 3$ are known. Using this classification, we give a classification of ternary extremal self-dual codes of length $ 28$. Up to equivalence, there are 6,931 such codes.


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Additional Information

Masaaki Harada
Affiliation: Department of Mathematical Sciences, Yamagata University, Yamagata 990–8560, Japan

Akihiro Munemasa
Affiliation: Graduate School of Information Sciences, Tohoku University, Sendai 980–8579, Japan

Boris Venkov
Affiliation: Steklov Institute of Mathematics at St. Petersburg, St. Petersburg 191011, Russia

DOI: https://doi.org/10.1090/S0025-5718-08-02194-7
Keywords: Extremal self-dual code, unimodular lattice, frame.
Received by editor(s): January 29, 2008
Received by editor(s) in revised form: June 9, 2008
Published electronically: October 24, 2008
Additional Notes: The work of the first and second authors was partially supported by the Sumitomo Foundation (Grant for Basic Science Research Projects, 050034).
Article copyright: © Copyright 2008 American Mathematical Society