Let C be an extremal Type III or IV code and \(D_{w}\) be the support design of C for weight w. We introduce the numbers, \(\delta (C)\) and s(C), as follows: \(\delta (C)\) is the largest integer t such that, for all weights, \(D_{w}\) is a t-design; s(C) denotes the largest integer t such that w exists and \(D_{w}\) is a t-design. Herein, we consider the possible values of \(\delta (C)\) and s(C).

中文翻译：

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关于极值 III 型和 IV 型码的支持 t 设计

令C为极值 III 或 IV 型代码，\(D_{w}\)为C对权重w的支持设计。我们引入数字\(\delta (C)\)和s ( C )，如下所示：\(\delta (C)\)是最大整数t，使得对于所有权重，\(D_{w} \)是一个t设计；s ( C ) 表示最大整数t使得w存在并且\(D_{w}\)是一个t设计。在这里，我们考虑\(\delta (C)\)的可能值和s ( C )。