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，并展示了其在两个方向上的应用。我们提出了从纽结着色出发构造纠错码的方法，通过一系列结果阐述了纽结性质如何转化为码参数。我们证明，利用纽结可以获得具有预定参数和高效解码算法的纠错码。