卡氏积码的MDR码和自对偶码

MDR codes and self-dual codes on Cartesian product codes

定义了12,,,ZrZrZrs上线性码C1,C2,,Cs的卡氏积码。利用子模同构定理,研究了在Zr1×Zr2××Zrs上卡氏积码C1×C2××Cs的秩与在12,,,ZrZrZrs码C1,C2,,Cs的秩的关系,借助这一关系,得到了MDR码的卡氏积仍为MDR码和自对偶码的卡氏积码也为自对偶码。

A Cartesian product code of the linear codes C1 … , C s in Zr1,… ,Zr was defined. According to the theorem of submodulo isomorphism, the relationship between the rank of the Cartesian product code C1 × C 2 ×…× Cs over Zr1 × 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.