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<p>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.</p>

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Knot theory and error-correcting codes

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年4月18日

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  • Altan B. Kılıç,
  • Anne Nijsten,
  • Ruud Pellikaan,
  • Alberto Ravagnani

摘要

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.