Abstract: In this talk, a necessary and sufficient condition for the existence of Type I {$m$-adic} constacyclic codes is given; further, for any given integer $s$, a necessary and sufficient condition for $s$ being a multiplier of a Type I polyadic constacyclic code is given. As applications, several corollaries are derived and some optimal codes from Type I polyadic constacyclic codes, including generalized Reed-Solomon codes and alternant MDS codes, are constructed.