Proof of the TuDeng Conjecture

[2608.14821] Proof of the TuDeng Conjecture Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Combinatorics arXiv:2608.14821 (math) [Submitted on 14 Aug 2026] Title: Proof of the TuDeng Conjecture Authors: Thomas W. Cusick View a PDF of the paper titled Proof of the TuDeng Conjecture, by Thomas W. Cusick View PDF HTML (experimental) Abstract: We give a complete proof of the 2011 Tu--Deng conjecture. We begin from its original modular pair-count formulation, prove an equivalent cyclic Hamming weight-drop formulation, and establish the exact transfer identity that connects this count with a two-variable matrix polynomial. The proof then reduces the conjecture to normalized inequalities for the coefficients of that polynomial. A 2011 conjecture by the author which came to be called the Cusick Conjecture (it is a consequence of the Tu--Deng Conjecture) was proved by K. Cheng in 2026. The proof in the present paper extends the cyclic deletion ideas of Cheng. The new ideas might be applicable to other problems. Comments: 15 pages Subjects: Combinatorics (math.CO) ; Information Theory (cs.IT) MSC classes: 94C10, 06E30, 94A60 Cite as: arXiv:2608.14821 [math.CO] (or arXiv:2608.14821v1 [math.CO] for this version) https://doi.org/10.48550/arXiv.2608.14821 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Thomas Cusick [ view email ] [v1] Fri, 14 Aug 2026 18:47:52 UTC (13 KB) Full-text links: Access Paper: View a PDF of the paper titled Proof of the TuDeng Conjecture, by Thomas W. Cusick View PDF HTML (experimental) TeX Source view license Current browse context: math.CO < prev | next > new | recent | 2026-08 Change to browse by: cs cs.IT math math.IT References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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