Knot Theory and Error-Correcting Codes

TL;DR

This paper explores the innovative connection between knot theory and algebraic coding theory, demonstrating how knot colorings can be used to construct error-correcting codes with specific properties and efficient decoding methods.

Contribution

It introduces a novel method to derive error-correcting codes from knot colorings, linking topological properties to coding parameters.

Findings

Knot colorings can be systematically used to generate error-correcting codes.

The paper provides methods to design codes with desired parameters based on knot properties.

An efficient decoding algorithm for these codes is developed.

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.