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Knot theory and error-correcting codes
Altan B Kılıç1, Anne Nijsten1, Ruud Pellikaan1
1Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, the Netherlands.
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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