摘要 : Let p be an odd prime, and k be an integer such that gcd(k,p) = 1. Using pairwise orthogonal idempotents gamma(1), gamma(2), gamma(3) of the ring R = F-p [u]/< u(k+1) - u >, with gamma(1)+ gamma(2) + gamma(3) = 1, R is decomposed ... 展开 Let p be an odd prime, and k be an integer such that gcd(k,p) = 1. Using pairwise orthogonal idempotents gamma(1), gamma(2), gamma(3) of the ring R = F-p [u]/< u(k+1) - u >, with gamma(1)+ gamma(2) + gamma(3) = 1, R is decomposed as R = gamma R-1 circle plus gamma R-2 circle plus gamma R-3, which contains the ring R = gamma F-1(p) circle plus gamma F-2(p) circle plus gamma F-3(p) as a subring. It is shown that, for lambda(0), lambda(k) is an element of F-p, lambda(0) + u(k)lambda(k) is an element of R, and it is invertible if and only if lambda(0) and lambda(0) + lambda(k) are units of F-p. In such cases, we study (lambda(0) + u(k)lambda(k))-constacyclic codes over R. We present a direct sum decomposition of (lambda(0) + u(k)lambda(k))-constacyclic codes and their duals, which provides their corresponding generators. Necessary and sufficient conditions for a (lambda(0) + u(k)lambda(k))-constacyclic code to contain its dual are obtained. As an application, many new quantum codes over F-p, with better parameters than existing ones, are constructed from cyclic and negacyclic codes over R. 收起