论文标题
在有限的通勤戒指上的$ \ ell $ dlips上
On the $\ell$-DLIPs of codes over finite commutative rings
论文作者
论文摘要
概括了线性互补双，线性互补对和代码船体，我们介绍了一些正面的integer $ \ ell $ \ ell $ \ ell $。在本文中，我们通过统一方法研究了$ r $的代码$ \ ell $ - 代码。此外，我们为在有限的交换frobenius环上存在非免费（或免费）$ \ ell $ dlip的代码提供了必要和充分的条件。此外，我们在有限的链环上获得了两个constacyclic代码的交点的发电机集，这有助于我们获得$ \ ell $ dlip的Constacyclic代码的重要特征。最后，有限链环上的constacyclic代码的$ \ ell $ - 用于构建新的纠缠量子误差校正（EAQEC）代码。
Generalizing the linear complementary duals, the linear complementary pairs and the hull of codes, we introduce the concept of $\ell$-dimension linear intersection pairs ($\ell$-DLIPs) of codes over a finite commutative ring $(R)$, for some positive integer $\ell$. In this paper, we study $\ell$-DLIP of codes over $R$ in a very general setting by a uniform method. Besides, we provide a necessary and sufficient condition for the existence of a non-free (or free) $\ell$-DLIP of codes over a finite commutative Frobenius ring. In addition, we obtain a generator set of the intersection of two constacyclic codes over a finite chain ring, which helps us to get an important characterization of $\ell$-DLIP of constacyclic codes. Finally, the $\ell$-DLIP of constacyclic codes over a finite chain ring are used to construct new entanglement-assisted quantum error correcting (EAQEC) codes.
