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Knot Theory and Error-Correcting Codes (2307.14882v2)
Published 27 Jul 2023 in cs.IT, math.AT, math.GN, and math.IT
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.