Classification of 3-(24, 12, 5) Designs and 24-Dimensional Hadamard Matrices
Classification of 3-(24, 12, 5) Designs and 24-Dimensional Hadamard Matrices
复制标题
3-(24, 12, 5) 设计和 24 维 Hadamard 矩阵的分类
DOI：
10.1016/0097-3165(81)90054-6
复制
发表时间：
1981
期刊：
影响因子：
--
通讯作者：
J. Leon
中科院分区：
文献类型：
--
作者：
N. Ito;J. Leon
最近，作者完成了3-（24，12，5）设计直到同构的分类.这些设计与24维阿达玛矩阵密切相关，设计工作导致了矩阵的分类等价。Hadamard矩阵的低维已确定以前霍尔[2-41。本文描述了分类中使用的技术，并对结果进行了总结。它提供了129个设计和59个矩阵中的每一个可以被构造的信息，并且它给出了每个设计和矩阵的自同构群的阶和轨道长度。矩阵的显式列表，以及它们的自同构群的生成置换，可以在[5]中找到。设计的相应数据见161。一般来说，3-（413.+ 4，21+ 2，L）设计D=（P，B）称为Hadamard设计（P和B分别表示点集和块集）。在这样的设计中，8A+ 6块的集合在互补下必然是闭合的[7];因此，如果6表示P-a，则B由4，l+ 3个块对01*={a，C}组成，我们称之为并行类。对于一个E P，我们让B，表示包含点a的块集。
Recently the authors completed the classification of 3-(24, 12, 5) designs up to isomorphism. These designs are closely related to 24-dimensional Hadamard matrices, and the work on designs leads to a classification of the matrices up to equivalence. Hadamard matrices of lower dimension had been determined previously by Hall [2-41. This article described the techniques used in the classification and contains a summary of the results. It provides information from which each of the 129 designs and 59 matrices can be constructed, and it gives the order and orbit lengths of the automorphism group of each design and matrix. An explicit list of the matrices, together with generating permutations for their automorphism groups, may be found in [5]. The corresponding data for designs appear in 161. In general, a 3-(413.+ 4, 21+ 2, L) design D=(P, B) is called a Hadamard design (P and B denote the sets of points and blocks, respectively). In such a design the set of 8A+ 6 blocks is necessarily closed under complementation [7]; thus, if 6 denotes P-a, B consists of 4, l+ 3 block pairs 01*={a, C}, which we term parallel classes. For a E P, we let B, denote the set of blocks containing the point a.