Abstract
Let \(C\) be an extremal binary doubly even self-dual code of length \(n\) and \(D_{w}\) be the support design of \(C\) for a weight \(w\). We introduce the two numbers \(\delta (C)\) and \(s(C)\): \(\delta (C)\) is the largest integer \(t\) such that, for all wight, \(D_{w}\) is a \(t\)-design; \(s(C)\) denotes the largest integer \(t\) such that there exists a \(w\) such that \(D_{w}\) is a \(t\)-design. In this paper, we consider the possible values of \(\delta (C)\) and \(s(C)\).
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Acknowledgments
The authors wish to thank Masaaki Kitazume for helpful discussions in Chiba University. The authors also thank Eiichi Bannai for providing the reference [9]. The second author would like to thank Masaaki Harada for useful discussions in Tohoku University. This work was supported by JSPS KAKENHI (22840003, 24740031).
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Communicated by V. D. Tonchev.
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Miezaki, T., Nakasora, H. An upper bound of the value of \(t\) of the support \(t\)-designs of extremal binary doubly even self-dual codes. Des. Codes Cryptogr. 79, 37–46 (2016). https://doi.org/10.1007/s10623-014-0033-7
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DOI: https://doi.org/10.1007/s10623-014-0033-7