In this paper, \(\delta \)-dual codes over finite commutative semi-simple rings are defined as a generalization of dual codes over finite commutative semi-simple rings. Some properties of \(\delta \)-dual codes are given. We present necessary and sufficient conditions for a \(\lambda \)-constacyclic code of length n to be \(\delta \)-self-dual, \(\delta \)-self-orthogonal, \(\delta \)-dual-containing, \(\delta \)-LCD over finite commutative semi-simple rings. We also study the \(\delta \)-dual of skew \(\Theta \)-\(\lambda \)-constacyclic codes over finite commutative semi-simple rings. Among others, we also give necessary and sufficient conditions for a skew \(\Theta \)-\(\lambda \)-constacyclic code of any length n to be \(\delta \)-self-dual, \(\delta \)-self-orthogonal, \(\delta \)-dual-containing, \(\delta \)-LCD over finite commutative semi-simple rings.

在本文中，有限交换半单环上的\(\delta\) -对偶码被定义为有限交换半单环上对偶码的推广。给出了\(\delta \) -对偶码的一些性质。我们提出了长度为n的\(\lambda \) -constacyclic 码是\(\delta \) -self-dual, \(\delta \) -self-orthogonal, \(\delta \)的充分必要条件-对偶，\(\delta \) -LCD 在有限交换半单环上。我们还研究了偏斜\(\Theta \) - \(\lambda \)的\(\delta \) -对偶-有限交换半单环上的恒循环码。其中，我们还给出了任意长度n的偏斜\(\Theta \) - \(\lambda \) -constacyclic 码为\(\delta \) -self-dual, \(\delta \) -自正交，\(\delta \) -对偶，\(\delta \) -有限交换半单环上的LCD。