We propose a new caching scheme where linear combinations of the file segments are cached at the users, for the cases where the number of files is no greater than the number of users. When a user requests a certain file in the delivery phase, the other file segments in the cached linear combinations can be viewed as interferences. The proposed scheme combines rank metric codes and maximum distance separable codes to facilitate the decoding and elimination of these interferences, and also to simultaneously deliver useful contents to the intended users. The performance of the proposed scheme can be explicitly evaluated, and we show that the tradeoff points achieved by this scheme can strictly improve known tradeoff inner bounds in the literature; for certain special cases, the new tradeoff points can be shown to be optimal.