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arXiv · 2307.14882

Knot Theory and Error-Correcting Codes

Altan B. Kilic·Anne Nijsten·Ruud Pellikaan·Alberto Ravagnani
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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.

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Altan B. Kilic, Anne Nijsten, Ruud Pellikaan, Alberto Ravagnani. 2023-07-27. Knot Theory and Error-Correcting Codes. https://doi.org/10.1007/s10623-025-01615-x

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