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.

翻译：在本文中,我们研究一些针对一定领域的双维循环和共周期的重复根代码,我们获得了这些代码及其双元的生成器矩阵和生成器多元体;我们还调查了这些代码及其双元体的生成器矩阵和生成器多元体;此外,我们证明,如果存在一个由单面的双维双元循环或共周期代码组成的无以复发的组合,那么就存在一个简单、二维双元循环或共周期代码的无以复现的组合,其参数至少与第一个家庭相同;此外,我们表明,Rajabi和Khashyarmanesh(2018年)以及Sepasdar和Khashyarmanesh(2016年)这两份文件的一些主要结果并不准确,因此,我们能找到其他必要的条件予以维持。