The automorphism group of the Zetterberg code Z of length 17 (also a quadratic residue code) is a rank three group whose orbits on the coordinate pairs determine two strongly regular graphs equivalent to the Paley graph attached to the prime 17. As a consequence, codewords of a given weight of Z are the characteristic vectors of the blocks of a PBIBD with two associate classes of cyclic type. More generally, this construction of PBIBDs is extended to quadratic residue codes of length \(\equiv 1 \pmod {8},\) to the adjacency codes of triangular and lattice graphs, and to the adjacency codes of various rank three graphs. A remarkable fact is the existence of 2-designs held by the quadratic residue code of length 41 for code weights 9 and 10.

长度为 17的 Zetterberg 码Z的自同构群（也是二次余数码）是一个秩为 3 的群，其坐标对上的轨道确定了两个强正则图等价于附加到素数 17 的佩雷图。因此，码字给定Z权重的特征向量是 PBIBD 块的特征向量，具有两个循环类型的关联类。更一般地说，PBIBD 的这种构造被扩展到长度为\(\equiv 1 \pmod {8},\) 的二次残差代码到三角形和点阵图的邻接代码，以及各种三阶图的邻接代码。一个值得注意的事实是存在由长度为 41 的二次残差代码持有的 2-designs，用于代码权重 9 和 10。