We study (Galois) linear complementary dual codes over mixed alphabets arising from finite chain rings. We give a characterization of when a given code is of We study (Galois) linear complementary dual codes over mixed alphabets arising from finite chain rings. We give a characterization of when a given code is of this type and when it is Galois invariant. Finally, this leads to a study of the Gray image of $\mathbb{F}_p\mathbb{F}_p[\theta]$-linear codes, where $p\in\{2; 3\}$ and $\theta\neq\theta^2=0$, that provides $\mathbb{F}_p$-linear complementary dual codes.
翻译：我们研究(伽洛瓦)线性补充双重编码,研究来自有限链环的混合字母。我们描述一个特定代码何时是我们研究(伽洛瓦)线性补充双重编码,研究来自有限链环的混合字母。我们描述一个特定代码何时是这种类型的,何时是加洛瓦的变异性。最后,这导致研究$mathbb{F\\\p\mathb{F\\\\mathb{p[\theta]$-线性代码的灰色图像,其中提供$p\in ⁇ 2;3 ⁇ $和$\theta\neq\theta2=0$,提供$mathbb{F\\\p$-线性补充双重编码。
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