Conjucyclic codes are an important and special family of classical error-correcting codes, which have been used to construct binary quantum error-correcting codes (QECCs). However, at present, the research on the conjucyclic codes is extremely insufficient. This paper will explore the algebraic structure of additive conjucyclic codes over
Fq2 for the first time. Mainly via the trace function from
Fq2 down
Fq, we will firstly build an isomorphic mapping between
q2-ary additive conjucyclic codes and
q-ary linear cyclic codes. Since the mapping preserves the weight and orthogonality, then the dual structure of these codes with respect to the alternating inner product will be described. Then a new construction of QECCs from conjucyclic codes can be obtained. Finally, the enumeration of
q2-ary additive conjucyclic codes of length
n and the explicit forms of their generator and parity-check matrices will be determined.