This paper builds a novel bridge between algebraic coding theory and mathematical knot theory, with applications in both directions. We give methods to construct error-correcting codes starting from the colorings of a knot, describing through a series of results how the properties of the knot translate into code parameters. We show that knots can be used to obtain error-correcting codes with prescribed parameters and an efficient decoding algorithm.

翻译：本文在代数编码理论与数学纽结理论之间构建了一座新颖的桥梁，并实现了两个方向的交叉应用。我们提出了从纽结着色出发构造纠错码的方法，通过一系列定理阐述了纽结特性如何转化为编码参数。研究表明，纽结可用于构造具有预设参数及高效译码算法的纠错码。