Double circulant LCD codes over \(\mathbb{Z}_4\) (Q2422190)

The authors show the existence of LCD codes over \(Z_4\) by using the CRT approach to quasi-cyclic codes. This approach is explained in Section 3. Afterwards, in Section 4 they give the number of LCD double circulant codes over \(Z_4\) (Theorem 3). Assuming that the Artin conjecture holds, the authors show that there exists an infinite family of double circulant LCD \(Z_4\)-codes with special properties (Theorem 5). In Table 1 (Section 6), some examples with best parameters are given. Finally in Section 7, the authors give some open problems, e.g.~the challenging problem to extend the results from \(Z_4\) to \(Z_{2^m}\).