Knot Theory and Error-Correcting Codes
Information Theory
2025-12-19 v2 Algebraic Topology
General Topology
math.IT
Abstract
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.
Cite
@article{arxiv.2307.14882,
title = {Knot Theory and Error-Correcting Codes},
author = {Altan B. Kilic and Anne Nijsten and Ruud Pellikaan and Alberto Ravagnani},
journal= {arXiv preprint arXiv:2307.14882},
year = {2025}
}