In this paper, we explore some properties of hulls of cyclic serial codes over a finite chain ring and we provide an algorithm for computing all the possible parameters of the Euclidean hulls of that codes. We also establish the average $p^r$-dimension of the Euclidean hull, where ${\mathbb{F}}_{p^r}$ is the residue field of R, as well as we give some results of its relative growth.

中文翻译：

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有限链环上循环序列码的外壳

在本文中，我们探讨了有限链环上循环串行码的外壳的一些特性，并提供了一种算法来计算该代码的欧几里得外壳的所有可能参数。我们还建立了平均${磷}^r$- 欧几里得船体的尺寸，其中 ${\mathbb{F}}_{{磷}^r}$是R的残差域，我们给出了它的相对增长的一些结果。