Alahmadi et al. ["Twisted centralizer codes", \emph{Linear Algebra and its Applications} {\bf 524} (2017) 235-249.] introduced the notion of twisted centralizer codes, $\mathcal{C}_{\mathbb{F}_q}(A,\gamma),$ defined as \[ \mathcal{C}_{\mathbb{F}_q}(A,\gamma)=\lbrace X \in \mathbb{F}_q^{n \times n}:~\ AX=\gamma XA\rbrace, \] for $A \in \mathbb{F}_q^{n \times n},$ and $\gamma \in \mathbb{F}_q.$ Moreover, Alahmadi et al. ["On the dimension of twisted centralizer codes", \emph{Finite Fields and Their Applications} {\bf 48} (2017) 43-59.] 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 $A.$
翻译：Alahmadi et al. [“Twisted Centralizer Code”,, \ emph{Linear Algebra 及其应用 \ bf 524} (2017 235-249)] (2017 235-249)] ] 引入了扭曲中央代码的概念, $\ mathcal{C ⁇ mathbb{F ⁇ q} (A,\ gammamama, 美元), 被定义为\\\\ mathcal{C\\\ mathb{C\ {C\\ mathb{F} F\ qq} (A, gamma, gamma, 美元), 被定义为[a,\ gammas calphrx 的维度, \ emph{Finaltime 及其应用} : (2017) Axqam XA\\ rbrres, \\\\, laxal basimal basion a basion a precal 和 a lical prilal press 范围, 。 Aqal 范围 范围, 范围 仅,, 仅, 仅 和直 范围, 范围 仅, 范围,, 仅,,, 提供 仅作为普通和直基 。
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