On symmetric nets and generalized Hadamard matrices from affine designs
On symmetric nets and generalized Hadamard matrices from affine designs
复制标题
关于仿射设计的对称网络和广义 Hadamard 矩阵
DOI：
10.1007/bf01220309
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发表时间：
2000
影响因子：
0.6
通讯作者：
V. Tonchev
中科院分区：
文献类型：
--
作者：
V. C. Mavron;V. Tonchev
对称网是仿射可分解设计，其对偶也是仿射的。结果表明，在同构意义下，恰好有四个对称(3, 3)-网（v = b = 27，k = 9），并且在3阶群上恰好有两个不等价的9×9广义阿达马矩阵。对称(3, 3)-网被发现是仿射可分解2-(27, 9, 4)设计的子网。68个不同构的仿射可分解2-(27, 9, 4)设计中有10个不是对称(3, 3)-子网的扩张，这提供了没有对称(q, q)-子网的仿射2-(q³, q², (q² - 1)/(q - 1))设计的首批实例。
Symmetric nets are affine resolvable designs whose duals are also affine. It is shown that. up to isomorphism, there are exactly four symmetric (3, 3)-nets (v=b=27,k=9), and exactly two inequivalent 9×9 generalized Hadamard matrices over the group of order 3. The symmetric (3, 3)-nets are found as subnets of affine resolvable 2-(27, 9, 4) designs. Ten of the 68 non-isomorphic affine resolvable 2-(27, 9, 4) designs are not extensions of symmetric (3, 3)-subnets, providing the first examples of affine 2-(q3, q2, q2−1/q−1) designs without symmetric (q, q)-subnets.