LCD and ACD codes over a noncommutative non-unital ring with four elements (Q2673775)

In this paper, the authors introduce LCD and ACD codes over a noncommutative non-unital ring \(E\) with four elements. They show that free LCD codes over \(E\) are directly related to binary LCD codes. Furthermore, they also characterize (left-) additive complementary dual codes over \(E\) in terms of their residue codes and their torsion codes. As a consequence, a natural generalization of LCD codes over \(E\) is provided. It is still an open problem to find a family of left-ACD codes over \(E\) with large minimum distances.