Research About The ?-constacyclic Codes On F_p^m[u,?]/<u^e>

In recent years,there.are rich results for the research of codes on finite com-mutative rings.However,there're not much researches on finite noncommutative rings.It is different from the commutative ring.Since the structure of noncom-mutative rings are more complicated,then the researches are more difficult.The ring Fpm[u,?]is a special noncommutative ring,where the multiplication on it is determined by Xa =?(a)X.Which made the researches on it are more difficult.Existing research shows that,there are some structures and properties of some codes on noncommutative rings can research by those on commutative rings.As a result,the range of research on noncommutative rings is gradually expanded.And the theory is increasingly enriched.In this thesis,we mainly research the structure of the left(right)?-constacyclic codes of length N on R=Fpm[u,?]/(ue).In fact,it is the structure of the left(right)ideal on S = R[x]/<xN-?A).And we proved that if it is satisfied the condition of theorem 3.1.1(theorem 3.1.2),the form of each left(right)ideal of S is unique.What's more,we obtained the the set of generators of the left(right)ideal of S.If I is the left ideal of S,then We have I=(F0(x),F1(x),...,Fe-1(x))L.Where Fi(x)=fi,i(x)ui+ fi,i+1(x)ui+1...+fi,e-1(x)ue-1=?fi,j(x)ui,fi,j(x)?Fpm[x],0?2?j<e-1.Analogously,If I is the right ideal of S,we have I=<Fo(x),F1(x),...,Fe-1(x)>R,where Fi(x)is the same as above.In this thesis,we also obtain the structure of the right(left)dual codes of left(right)cyclic codes of length N on R.And the thesis figures out the connection between the generator polynomials of a left(right)?-constacyclic code and those of its right(left)dual code.Finally,we make it clear that the connection between the left(right)?-con-stacyclic codes and right(left)constacyclic codes on R2 = Fpm[u,?]/(u2)and study the self-dual left(right)?-constacyclic codes over R2.