Homogeneous metric and matrix product codes over finite commutative principal ideal rings (Q1987108)

In this paper, the authors find out a necessary and sufficient condition for the homogeneous distance on an arbitrary finite commutative principal ideal ring to be a metric, which generalizes the distance introduced in [\textit{I. Constantinescu} and \textit{W. Heise}, Probl. Inf. Transm. 33, No. 3, 208--213 (1997; Zbl 0977.94055); translation from Probl. Peredachi Inf. 33, No. 3, 22--28 (1997)]. After that, they investigate the lower bound of homogeneous distances of matrix product codes (and their duals) over any finite principal ideal ring where the homogeneous distance is a metric, generalizing [\textit{Y. Fan} et al., Finite Fields Appl. 29, 247--267 (2014; Zbl 1332.94112)].