论文标题
双重固定代码在两个有限的交换链环上
Double Constacyclic Codes over Two Finite Commutative Chain Rings
论文作者
论文摘要
在两个特殊有限的交换链环上具有两个循环结构的代码，例如$ {\ bbb z} _2 {\ bbb z} _4 $ - 添加循环代码和分数索引的准循环代码，是分数索引等的准代码。在本文中，我们将研究扩展到两个方向：我们考虑了任何两个有限的交换链环，具有圆形同态，并考虑双重构造结构。我们在两个有限的交换链环上构建了广泛的双骨constacyclic代码。并且，开发一种适合于字段上的准环状代码的概率方法，我们证明了两个有限的交换链环上的双constacyclic代码在渐近上是好的。
Many kinds of codes which possess two cycle structures over two special finite commutative chain rings, such as ${\Bbb Z}_2{\Bbb Z}_4$-additive cyclic codes and quasi-cyclic codes of fractional index etc., were proved asymptotically good. In this paper we extend the study in two directions: we consider any two finite commutative chain rings with a surjective homomorphism from one to the other, and consider double constacyclic structures. We construct an extensive kind of double constacyclic codes over two finite commutative chain rings. And, developing a probabilistic method suitable for quasi-cyclic codes over fields, we prove that the double constacyclic codes over two finite commutative chain rings are asymptotically good.
