Researches On Skew Constancyclic Codes And Quantum Codes Over Some Finite Rings

In this paper,we research some related problems of skew consta-cyclic codes over the finite rings R=R+uR + vR + uvR(u2 = u,v2 =v,vu = vu),R1=F2m +?F2m+?F2m+??F2m(?2=0,??=??)and constructed quantum codes by(1 + 2?)-constacyclic codes over R2 = Fp + ?Fp(?2 =-?).The specific concent as follows:(1)The first part,we mainly study skew constacyclic codes over the ring R.Firstly,we obtain the generator polynomials of skew consta-cyclic codes over R by direct sum decomposition.Secondly,we obtain a necessary and sufficient condition that the dual codes of the skew constacyclic codes over R is skew constacyclic.Hence the generation polynomial of the dual code of the skew constacyclic codes is given.(2)The second part,we mainly study skew constacyclic codes with lengh n over the ring R1.Firstly,we obtain that the Gray image of skew constacyclic codes with length n over R1 is skew quasi-cyclic code of index 2 witn length 4n.Secondly,the properties of Hermitiam dual codes and their generation polynomials are given.(3)The third part,we mainly study constructed quantum codes by(1 + 2?)-constacyclic codes over R2.Firstly,the well Gray map on ring R2 is defined,and the proporties of the Gray image of(1 + 2?)-constacyclic C are discussed.Secondly,the dual properties of(1 + 2?)-constacyclic codes are discussed and the existence theorem of quantum codes under certain conditions are obtained with parameter[[2n,2k-2n,dG]]p and some exemples are given.