Abstract

We previously have developed two methods for constructing codes and designs from finite simple groups. In a recent paper we introduced a new method (Method 3) for constructing codes and designs from fixed points of elements of finite transitive groups. This new method together with background material and results required from finite groups, permutation groups and representation theory were discussed fully in that paper. The main aim of this paper is to apply the method to the fixed points of involutions of the Alternating group A_n (for n ≥ 5) on its action on Ω, 2-subsets (or duads) Γ^{2} of a set Γ of size n.

中文翻译：

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An 对合的设计和代码

摘要

我们之前已经开发了两种从有限单组构造代码和设计的方法。在最近的一篇论文中，我们介绍了一种新方法（方法 3），用于从有限传递群的元素的不动点构造代码和设计。该文对这种新方法以及有限群、置换群和表示论所需的背景材料和结果进行了充分讨论。本文的主要目的是将该方法应用于交替群A _n（对于n ≥ 5）对集 Γ 的 Ω、2-子集（或对偶）Γ ^{2}的作用的对合不动点大小为n。