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On the support t-designs of extremal Type III and IV codes
Applicable Algebra in Engineering, Communication and Computing ( IF 0.6 ) Pub Date : 2022-07-20 , DOI: 10.1007/s00200-022-00571-6 Tsuyoshi Miezaki , Hiroyuki Nakasora
中文翻译:
关于极值 III 型和 IV 型码的支持 t 设计
更新日期:2022-07-20
Applicable Algebra in Engineering, Communication and Computing ( IF 0.6 ) Pub Date : 2022-07-20 , DOI: 10.1007/s00200-022-00571-6 Tsuyoshi Miezaki , Hiroyuki Nakasora
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:
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 )。