Strong difference families of special types are introduced to produce new relative difference families from the point of view of both asymptotic existences and concrete examples. As applications, group divisible designs of type $30^u$ with block size $6$ are discussed, $r$-rotational balanced incomplete block designs with block size $6$ are derived for $r\in\{6,10\}$, and several classes of optimal optical orthogonal codes with weight $5$, $6$, $7$, or $8$ are obtained.

中文翻译：

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特殊类型的强差分族

引入特殊类型的强差分族，从渐近存在和具体实例的角度产生新的相对差分族。作为应用，讨论了块大小为 $6$ 的 $30^u$ 类型的群可分设计，推导出 $r$-块大小为 $6$ 的旋转平衡不完全块设计 $r\in\{6,10\}$，并且得到了几类权重为$5$、$6$、$7$或$8$的最优光学正交码。