New Classes Of Codes Over [Rq,P,M =Z(Pm)[U(1),U(2), ..., U(Q)] / < U(I)(2)=0, U(I)U(J) = U(J)U(I)> And Their Applications

In this paper, we consider the construction of new classes of linear codes over the ring R-q,R-p,R-m=Z(pm)[u(1),u(2),...u(q)] / < u(i)(2) = 0, u(i)u(j) = u(j)u(i)> for i not equal j and 1 <= i, j <= q. The simplex and MacDonald codes of types alpha and beta are obtained over R-q,R-p,R-m. We characterize some linear codes over Z(p)(m) that are the torsion codes and Gray images of these simplex and MacDonald codes, and determine the minimal codes.