Two infinite families of two-weight codes over Z2m

In this paper, we first construct two infinite families of new two-weight codes over Z(2m) with respect to homogeneous metric and Lee metric by their generator matrices, which generalizes the results in Shi et al (Des Codes Cryptogr 88(3):1-13, 2020) from two different directions. We construct some optimal codes over Z(2m) and prove all codes in one of these two families are self-orthogonal. Finally, we determine the linearity of the Gray images of the codes we constructed for Lee metric completely.

Automated summary

In this paper, we construct two infinite families of new two-weight codes over Z(2m) by their generator matrices, which generalize the previous results. We also construct some optimal codes and prove that all codes in one of the families are self-orthogonal. Finally, we determine the linearity of the Gray images of the codes constructed for Lee metric.