Let A be an arbitrary alphabet and let θ be an (anti-)automorphism of $A^{⁎}$ (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under θ (θ-invariant for short) that is, languages L satisfying $\theta (L)\subseteq L$. We establish an extension of the famous defect theorem. With regard to the so-called notion of completeness, we provide a series of examples of finite complete θ-invariant codes. Moreover, we establish a formula which allows to embed any non-complete θ-invariant code into a complete one. As a consequence, in the family of the so-called thin θ-invariant codes, maximality and completeness are two equivalent notions.

设A为任意字母，设θ为的（反）自同构${\mathrm{一种}}^{⁎}$（根据定义，这种对应关系由字母的排列确定）。本文讨论的是在θ下不变的集合（简称θ-不变），即语言L满足$\theta （\mathrm{大号}）\subseteq \mathrm{大号}$。我们建立了著名的缺陷定理的扩展。关于完整性的概念，我们提供了一系列有限的完整θ不变码的例子。此外，我们建立了一个公式，可以将任何不完整的θ不变代码嵌入到完整的代码中。结果，在所谓的薄θ不变代码族中，最大性和完整性是两个等价的概念。