In this paper we study the structure and properties of additive right and left polycyclic codes induced by a binary vector $a$ in $\mathbb{F}_{2}^{n}.$ 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 $C$ is a right polycyclic code induced by a vector $a\in \mathbb{F}_{2}^{n}$, then the Hermitian dual of $C$ is a sequential code induced by $a.$ As an application of these codes, we present examples of additive right polycyclic codes over $\mathbb{F}_{4}$ 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 $\mathbb{F}_{4}.$
翻译：在本文中,我们研究了由二进制矢量($\mathbb{F ⁇ 2 ⁇ n}.$)引发的添加式右和左多环代码的结构和特性。我们发现了产生式多环代码和这些代码的基点。我们还研究了这些代码的不同双重代码。特别是,我们表明,如果$C是由矢量($a\in\mathbb{F ⁇ 2 ⁇ n}$)引发的正确的多环代码,那么赫米提双倍值($C$)是由$($)引发的顺序代码。作为这些代码的应用,我们举出了超过$\mathb{F ⁇ 4}美元($)的添加式右多环代码的例子,其代码比可比的最佳线性代码还要多,以及从超过$\mathb{F ⁇ 4}的添加式右环代码中获得的最佳双线代码和最佳量代码。
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