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Construction of extremal Type II Z2k-codes

Institution:	1. School of Mathematical Sciences, Hebei Workstation for Foreign Academicians, Hebei Normal University, Shijiazhuang 050024, PR China;2. Chelyabinsk State University, 129 Bratiev Kashirinykh st., Chelyabinsk 454021, Russia;3. Department of Mathematics, University of British Columbia, Vancouver V6T 1Z2, Canada;1. Korea Institute for Advanced Study (KIAS), Republic of Korea;2. Discrete Mathematics Group, Institute for Basic Science (IBS), Republic of Korea;3. University of Science, Vietnam National University, Hanoi, Viet Nam;1. School of Mathematics, Shandong University, Jinan, 250100, China;2. Hubei Key Laboratory of Applied Mathematics, School of Cyber Science and Technology, Hubei University, Wuhan, 430062, China;3. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, China

Abstract:	We give methods for constructing many self-dual $Z_{m}$ -codes and Type II $Z_{2 k}$ -codes of length 2n starting from a given self-dual $Z_{m}$ -code and Type II $Z_{2 k}$ -code of length 2n, respectively. As an application, we construct extremal Type II $Z_{2 k}$ -codes of length 24 for $k = 4, 5, \dots, 20$ and extremal Type II $Z_{2 k}$ -codes of length 32 for $k = 4, 5, \dots, 10$ . We also construct new extremal Type II $Z_{4}$ -codes of lengths 56 and 64.

Keywords:	Self-dual code Type II code Extremal Type II code
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