Knot Theory and Error-Correcting Codes
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866912771489136640 |
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| author | Kilic, Altan B. Nijsten, Anne Pellikaan, Ruud Ravagnani, Alberto |
| author_facet | Kilic, Altan B. Nijsten, Anne Pellikaan, Ruud Ravagnani, Alberto |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_14882 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Knot Theory and Error-Correcting Codes Kilic, Altan B. Nijsten, Anne Pellikaan, Ruud Ravagnani, Alberto Information Theory Algebraic Topology General Topology 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. |
| title | Knot Theory and Error-Correcting Codes |
| topic | Information Theory Algebraic Topology General Topology |
| url | https://arxiv.org/abs/2307.14882 |