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There are various metrics for researching error-correcting codes. Especially,high-density data storage system gives the existence of inconsistency for thereading and writing process. The symbol-pair metric is motivated for outputsthat have overlapping pairs of symbols in a certain channel. TheRosenbloom-Tsfasman (RT) metric is introduced since there exists a problem thatis related to transmission over several parallel communication channels withsome channels not available for the transmission. In this paper, we determinethe minimum symbol-pair weight and RT weight of repeated-root cyclic codes over$\mathfrak R=\Bbb F_{p^m}[u]/\langle u^4\rangle$ of length $n=p^k$. For thedetermination, we explicitly present third torsional degree for all differenttypes of cyclic codes over $\mathfrak R$ of length $n$.

Determination for minimum symbol-pair and RT weights via torsional degrees of repeated-root cyclic codes