We consider linear codes over a field in which the error values are restricted to a subgroup of its unit group. This scenario captures Lee distance codes as well as codes over the Gaussian or Eisenstein integers. Codes correcting restricted errors gained increased attention recently in the context of code-based cryptography. In this work we provide new constructions of codes over the Gaussian or Eisenstein integers correcting two or three errors. We adapt some techniques from Roth and Siegel's work on codes for the Lee metric. We propose two construction methods, which may be seen of geometric and algebraic flavor, respectively.

翻译：我们考虑在某个域上的线性编码，其中错误值被限制在该域单位群的一个子群内。这一场景涵盖了Lee距离编码以及在高斯整数或艾森斯坦整数上的编码。纠正受限错误的编码近年来在基于编码的密码学背景下受到越来越多的关注。在本工作中，我们提出了能够纠正两个或三个错误的高斯整数或艾森斯坦整数编码的新构造。我们借鉴了Roth和Siegel在Lee度量编码研究中的一些技术。我们提出了两种构造方法，可分别视为具有几何风格和代数风格。