Abstract

We previously have developed two methods (Key–Moori Methods 1 and 2) for constructing codes and designs from finite groups (mostly simple finite groups). In this article, we introduce a new method (Method 3) for constructing codes and designs from fixed points of elements of finite transitive groups. We first discuss background material and results required from finite groups, permutation groups and representation theory. The main aim of this article is to discuss this new method and give some examples by applying it to the sporadic simple groups HS and J ₂. In subsequent papers, we aim to apply it to several other simple groups.

中文翻译：

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有限群不动点的设计与编码

摘要

我们以前已经开发了两种方法（Key-Moori方法1和2），用于从有限组（主要是简单有限组）构造代码和设计。在本文中，我们介绍了一种从有限可及群的元素的不动点构造代码和设计的新方法（方法3）。我们首先讨论背景材料和有限组，置换组和表示理论所需的结果。本文的主要目的是讨论这种新方法，并通过将其应用于零星的简单组HS和J ₂给出一些示例。在随后的论文中，我们旨在将其应用于其他几个简单的组。