论文标题
单侧重复根二维循环和constacyclic代码
One-Sided Repeated-Root Two-Dimensional Cyclic and Constacyclic Codes
论文作者
论文摘要
在本文中，我们研究了有限字段上的一些重复的二维循环和constacyclic代码，$ f = \ mathbb {f} _q $。我们获得了这些代码及其双重的发电机矩阵和发电机多项式。我们还调查了此类代码何时是自动划分的。此外，我们证明，如果存在一个渐近良好的单方面重复根二维循环或constacyclic代码的家庭，则存在一个渐近良好的简单根部二维环状或constacyclic代码的渐近族，具有至少与第一个家庭一样好的。此外，我们表明论文Rajabi和Khashyarmanesh（2018）以及Sepasdar和Khashyarmanesh（2016）的几个主要结果不准确，并且找到了需要其他条件才能持有。
In this paper, we study some repeated-root two-dimensional cyclic and constacyclic codes over a finite field $F=\mathbb{F}_q$. We obtain the generator matrices and generator polynomials of these codes and their duals. We also investigate when such codes are self-dual. Moreover, we prove that if there exists an asymptotically good family of one-sided repeated-root two-dimensional cyclic or constacyclic codes, then there exists an asymptotically good family of simple root two-dimensional cyclic or constacyclic codes with parameters at least as good as the first family. Furthermore, we show that several of the main results of the papers Rajabi and Khashyarmanesh (2018) and Sepasdar and Khashyarmanesh (2016) are not accurate and find other conditions needed for them to hold.
