On the existence of extremal Type II $\mathbb {Z}_{2k}$-codes
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Abstract:
For lengths $8$, $16$, and $24$, it is known that there is an extremal Type II $\mathbb {Z}_{2k}$-code for every positive integer $k$. In this paper, we show that there is an extremal Type II $\mathbb {Z}_{2k}$-code of lengths $32,40,48,56$, and $64$ for every positive integer $k$. For length $72$, it is also shown that there is an extremal Type II $\mathbb {Z}_{4k}$-code for every positive integer $k$ with $k \ge 2$.References
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Additional Information
- Masaaki Harada
- Affiliation: Department of Mathematical Sciences, Yamagata University, Yamagata 990–8560, Japan
- Email: mharada@sci.kj.yamagata-u.ac.jp
- Tsuyoshi Miezaki
- Affiliation: Department of Mathematics, Oita National College of Technology, 1666 Oaza-Maki, Oita, 870–0152, Japan
- Address at time of publication: Faculty of Education, Art and Science, Yamagata University, Yamagata 990-8560, Japan
- Email: miezaki@e.yamagata-u.ac.jp
- Received by editor(s): May 31, 2012
- Received by editor(s) in revised form: July 24, 2012
- Published electronically: July 24, 2013
- © Copyright 2013 American Mathematical Society
- Journal: Math. Comp. 83 (2014), 1427-1446
- MSC (2010): Primary 94B05; Secondary 11H71, 11F11
- DOI: https://doi.org/10.1090/S0025-5718-2013-02750-0
- MathSciNet review: 3167465
Dedicated: In memory of Boris Venkov