Research On Skew Cyclic Codes Over Two Classes Of Finite Rings

Skew cyclic codes are studied on the basis of cyclic codes.By introducing automorphism over rings,the algebraic structure of skew cyclic codes is different from that of cyclic codes.Since the skew cyclic code was first studied,it has been widely concerned by scholars.Through skew cyclic codes,many better error-correcting codes can be obtained,such as constructing DNA codes based on skew cyclic codes and getting the relationship between DNA codes and cyclic codes through Gray mapping.The main contents of this dissertation are as follows:(1)For a given automorphism map over ring R = F_p+vF_p,the center is R[x;θ],and then the generator of skew cyclic codes over ring R is discussed.(2)The properties of skew cyclic codes over ring F_pR are studied,and the algebraic structure of skew cyclic codes over ring F_pR is obtained.(3)The relationship between skew cyclic codes on ring F_pR and cyclic codes and quasi-cyclic codes is given.(4)The properties of Gray images of skew cyclic codes over ring F_pR are studied.(5)The algebraic structure and properties of skew constant cyclic codes over ring F_pR are studied.