We introduce and discuss an elementary tool from representation theory of finite groups for constructing linear codes invariant under a given permutation group G. The tool gives theoretical insight as well as a recipe for computations of generator matrices and weight distributions. In some interesting cases a classification of code vectors under the action of G can be obtained. As an explicit example a class of binary codes is studied extensively which is closely related to the class of binary codes associated to triangular graphs. A second explicit application is related to the action of the Mathieu simple group ${\mathrm{M}}_{24}$ on the set of octads giving many binary codes of length 759 with interesting properties. We also obtain new alternative proofs for several other theorems and construct several new codes invariant under various subgroups of the Conway simple group ${\mathrm{Co}}_1$.

我们介绍并讨论了有限群表示理论中的一种基本工具，用于构造给定置换群G下的线性代码不变。该工具提供了理论见解以及计算生成器矩阵和权重分布的方法。在一些有趣的情况下，可以获得G作用下的代码向量分类。作为一个明确的例子，广泛研究了一类二进制代码，它与与三角图相关的二进制代码类密切相关。第二个显式应用与 Mathieu 单群的作用有关${\mathrm{米}}_{24}$在八元组上，给出了许多具有有趣特性的长度为 759 的二进制代码。我们还为其他几个定理获得了新的替代证明，并在康威单群的各个子群下构造了几个新代码不变${\mathrm{公司}}_1$.