Conjucyclic codes are part of a family of codes that includes cyclic, constacyclic, and quasi-cyclic codes, among others. Despite their importance in quantum error correction, they have not received much attention in the literature. This paper focuses on additive conjucyclic (ACC) codes over $\mathbb{F}_4$ and investigates their properties. Specifically, we derive the duals of ACC codes using a trace inner product and obtain the trace hull and its dimension. Also, establish a necessary and sufficient condition for an additive code to have a complementary dual (ACD). Additionally, we identify a necessary condition for an additive conjucyclic complementary pair of codes over $\mathbb{F}_4$. Furthermore, we show that the trace code of an ACC code is cyclic and provide a condition for the trace code of an ACC code to be LCD. To demonstrate the practical application of our findings, we construct some good entanglement-assisted quantum error-correcting (EAQEC) codes using the trace code of ACC codes.

翻译：共轭循环码是一类包含循环码、常循环码、准循环码等在内的码族。尽管它们在量子纠错中具有重要价值，但文献中对其关注尚不充分。本文聚焦于$\mathbb{F}_4$上的加法共轭循环（ACC）码，并研究其性质。具体而言，我们利用迹内积推导ACC码的对偶码，获得迹壳及其维数。同时，建立加法码具有互补对偶（ACD）的充要条件。此外，我们识别出$\mathbb{F}_4$上加法共轭循环互补码对的必要条件。进一步，证明ACC码的迹码是循环码，并给出ACC码的迹码为LCD码的条件。为展示研究成果的实际应用，我们利用ACC码的迹码构造了若干优良的纠缠辅助量子纠错（EAQEC）码。