{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/binary-codes-that-do-not-preserve-primitivity","title":"Binary codes that do not preserve primitivity","arxiv_id":"2203.11341","date":"2022-03-21","proceeding":null,"authors":["Štěpán Holub","Martin Raška","Štěpán Starosta"],"abstract":"A code $X$ is not primitivity preserving if there is a primitive list ${\\mathbf w} \\in {\\tt lists} X$ whose concatenation is imprimitive. We formalize a full characterization of such codes in the binary case in the proof assistant Isabelle/HOL. Part of the formalization, interesting on its own, is a description of $\\{x,y\\}$-interpretations of the square $xx$ if $|y| \\leq |x|$. We also provide a formalized parametric solution of the related equation $x^jy^k = z^\\ell$.","url_abs":"https://arxiv.org/abs/2203.11341v1","url_pdf":"https://arxiv.org/pdf/2203.11341v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"binary-codes-that-do-not-preserve-primitivity","repo_url":"https://gitlab.com/formalcow/combinatorics-on-words-formalized","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}