A Cartesian product code of the linear codes C1

C s in 1

Z r Z rs was defined. According to the theorem of submodulo isomorphism

the relationship between the rank of the Cartesian product code C1 × C 2 × × Cs over Z r1 × Z r2 × × Zrsand C1

C 2

C scodes overZ r1 × Z r2 × × Zrs were studied. Furthermore

it can include that Cartesian product code of MDS codes is MDR code

and so do the self -dual.