The covering problem for finite rings with respect to the RT-metric

In this work, the cardinality of the minimal R -covers of finite rings with respect to the RT-metric is established. By generalizing the result in Nakaoka and dos Santos (2010) [1], the minimal cardinalities of 0-short coverings of finite chain rings are calculated. The connection between R -short coverings of rings with respect to the RT-metric and the 0-short coverings of rings is demonstrated, and with the help of this connection, the problem of finding the minimal cardinalities of R -short coverings of finite chain rings is solved.