Knot theory and error-correcting codes
Altan B. Kılıç, Anne Nijsten, Ruud Pellikaan, Alberto Ravagnani · Designs Codes and Cryptography · 2025
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.