We survey the notion and history of error-correcting codes and the algorithms needed to make them effective in information transmission. We then give some basic as well as more modern constructions of, and algorithms for, error-correcting codes that depend on relatively simple elements of applied algebra. While the role of algebra in the constructions of codes has been widely acknowledged in texts and other writings, the role in the design of algorithms is often less widely understood, and this survey hopes to reduce this difference to some extent.

翻译：本文综述了纠错码的概念与历史，以及使其在信息传输中有效运作所需的算法。随后，我们介绍了一些基于应用代数相对简单要素的纠错码的基本及现代构造方法及其相关算法。尽管代数在码构造中的作用已在教材和其他文献中得到广泛认可，但其在算法设计中的作用往往未被充分理解，本综述旨在一定程度上缩小这一认知差距。