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Knot Theory and Error-Correcting Codes
July 27, 2023 Β· Declared Dead Β· π Designs, Codes and Cryptography
"No code URL or promise found in abstract"
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Authors
Altan B. Kilic, Anne Nijsten, Ruud Pellikaan, Alberto Ravagnani
arXiv ID
2307.14882
Category
cs.IT: Information Theory
Cross-listed
math.AT,
math.GN
Citations
0
Venue
Designs, Codes and Cryptography
Last Checked
4 months ago
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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