A Cartesian product code of the linear codes C 1,…,Cs in was defined.According to the theorem of submodulo isomorphism,the relationship between the rank of the Cartesian product code C1×C2×…×Cs overand C1,C2,…,Cscodes over were studied.Furthermore,it can include that Cartesian product code of MDS codes is MDR code,and so do the self -dual.