文摘
In this short paper, we determine the minimal generating set of 1-generator generalized quasi-cyclic codes over \(\mathbb {Z}_{4}\). We also determine their rank and introduce a lower bound for the minimum distance of free 1-generator generalized quasi-cyclic codes. Further, we construct some new \(\mathbb {Z}_{4}\)-linear codes and we obtain some good binary nonlinear codes using the usual Gray map.