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

Quaternary Conjucyclic Codes with an Application to EAQEC Codes