Abstract
It is known that extremal doubly-even self-dual codes of length \(n\equiv 8\) or \(0\ (\mathrm {mod}\ 24)\) yield 3- or 5-designs respectively. In this paper, by using the generator matrices of bordered double circulant doubly-even self-dual codes, we give 3-(n, k; m)-SEEDs with (n, k, m) \(\in \{(32,8,5), (56,12,9), (56,16,9), (56,24,9), (80,16,52)\}\). With the aid of computer, we obtain 22 generator matrices of bordered double circulant doubly-even self-dual codes of length 48, which enable us to get 506 mutually disjoint 5-(48, k, \(\lambda \)) designs for (k, \(\lambda \))=(12, 8),(16, 1356),(20, 36176). Moreover, this implies 5-(48, k; 506)-SEEDs for \(k=12, 16, 20, 24\).
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The authors would like to thank the editor and the two anonymous referees for their helpful comments. Supported by NSFC Grant 11271042 and the Fundamental Research Funds for the Central Universities 2011JBZ012
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Communicated by V. D. Tonchev.
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Fang, J., Chang, Y. Mutually disjoint t-designs and t-SEEDs from extremal doubly-even self-dual codes. Des. Codes Cryptogr. 73, 769–780 (2014). https://doi.org/10.1007/s10623-013-9825-4
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DOI: https://doi.org/10.1007/s10623-013-9825-4