Let p be a prime of the form \(p=mt+1\), where integers \(t\ge 1, m\ge 2\) and \(R_m=\mathbb {F}_p[u]/\langle u^m-1\rangle .\) Thus, \(R_m\) is a finite commutative non-chain ring. For a given unit \(\lambda \in R_m\), we study \(\lambda \)-constacyclic codes of length n over \(R_m\). The necessary and sufficient conditions for these codes to contain their Euclidean duals are determined. As an application from dual-containing \(\lambda \)-constacyclic codes over \(R_m\), for \(m=2,3,4\), we obtain many new quantum codes that improve on the known existing quantum codes.

令p为\（p = mt + 1 \）形式的素数，其中整数\（t \ ge 1，m \ ge 2 \）和\（R_m = \ mathbb {F} _p [u] / \ langle u ^ m-1 \ rangle。\）因此，\（R_m \）是有限的可交换非链环。对于给定的单位\（\ lambda \ in R_m \），我们研究\（\ lambda \）-在\（R_m \）上长度为n的常数循环码。确定这些代码包含其欧几里得对偶的必要和充分条件。作为来自双重包含\（\ lambda \）- \（R_m \）上的常量代码的应用程序，对于\（m = 2,3,4 \），我们获得了许多新的量子代码，它们在已知的现有量子代码上有所改进。