Alahmadi et al. (2017) [2] introduced the notion of twisted centralizer codes, ${\mathcal{C}}_{{\mathbb{F}}_q}(A,\gamma )$, defined as${\mathcal{C}}_{{\mathbb{F}}_q}(A,\gamma )=\{X\in {\mathbb{F}}_q^{n\times n}:AX=\gamma XA\},$ for $A\in {\mathbb{F}}_q^{n\times n}$, and $\gamma \in {\mathbb{F}}_q$. Moreover, Alahmadi et al. (2017) [3] also investigated the dimension of such codes and obtained upper and lower bounds for the dimension, and the exact value of the dimension only for cyclic or diagonalizable matrices A. Generalizing and sharpening Alahmadi et al.'s results, in this paper, we determine the exact value of the dimension as well as provide an algorithm to construct an explicit basis of the codes for any given matrix A.

中文翻译：

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基于扭曲的扶正器代码的大小和尺寸

Alahmadi等。（2017）[2]介绍了扭曲扶正器代码的概念，${\mathcal{C}}_{{\mathbb{F}}_q}（\mathrm{一种}，\gamma ）$， 定义为${\mathcal{C}}_{{\mathbb{F}}_q}（\mathrm{一种}，\gamma ）=\{X\in {\mathbb{F}}_q^{ñ\times ñ}：\mathrm{一种}X=\gamma X\mathrm{一种}\}，$ 为了 $\mathrm{一种}\in {\mathbb{F}}_q^{ñ\times ñ}$， 和 $\gamma \in {\mathbb{F}}_q$。此外，Alahmadi等。（2017）[3]也研究了此类代码的维数，并获得了维数的上下界，并且仅对于循环或对角化矩阵A才获得了维数的精确值。泛化和锐化Alahmadi等人的结果，在本文中，我们确定了尺寸的精确值，以及提供一种算法来构造码的明确基础对于任何给定矩阵甲。