In this paper, we study the structure and properties of additive right and left polycyclic codes induced by a binary vector \begin{document}$ a $\end{document} in \begin{document}$ \mathbb{F}_{2}^{n}. $\end{document} We find the generator polynomials and the cardinality of these codes. We also study different duals for these codes. In particular, we show that if \begin{document}$ C $\end{document} is a right polycyclic code induced by a vector \begin{document}$ a\in \mathbb{F}_{2}^{n} $\end{document}, then the Hermitian dual of \begin{document}$ C $\end{document} is a sequential code induced by \begin{document}$ a. $\end{document} As an application of these codes, we present examples of additive right polycyclic codes over \begin{document}$ \mathbb{F}_{4} $\end{document} with more codewords than comparable optimal linear codes as well as optimal binary linear codes and optimal quantum codes obtained from additive right polycyclic codes over \begin{document}$ \mathbb{F}_{4}. $\end{document}

在本文中，我们研究了由二进制向量诱导的加法左右多环码的结构和性质\begin{document}$ 一个 $\end{document}在\begin{文档}$ \mathbb{F}_{2}^{n}。$\end{文档}我们找到了生成多项式和这些代码的基数。我们还研究了这些代码的不同对偶。特别是，我们证明如果\begin{文档}$ C $\end{文档}是由向量诱导的右多环码\begin{document}$ a\in \mathbb{F}_{2}^{n} $\end{document}，然后是 Hermitian 对偶\begin{文档}$ C $\end{文档}是由以下引起的顺序代码\begin{document}$ 一个。$\end{文档}作为这些代码的应用，我们给出了加法右多环代码的例子\begin{文档}$ \mathbb{F}_{4} $\end{文档}具有比可比较的最优线性码以及最优二进制线性码和从加法右多环码获得的最优量子码更多的码字\begin{文档}$ \mathbb{F}_{4}。$\end{文档}