Spectral Theory of Semisimple Bivariate Bicycle Codes

[2608.27565] Spectral Theory of Semisimple Bivariate Bicycle Codes Skip to main content Search Submit Donate Log in Quantum Physics arXiv:2608.27565 (quant-ph) [Submitted on 27 Aug 2026] Title: Spectral Theory of Semisimple Bivariate Bicycle Codes Authors: Eric Sabo , Mahir Bilen Can , David Marquis View PDF HTML (experimental) Abstract: Extending the classical theory of two-dimensional cyclic codes, we develop an algebraic approach to bivariate bicycle codes. Using Frobenius-orbit idempotents, formulas for logical dimensions are derived and lower bounds on minimum distances are established. A systematic theory of code symmetries is formulated to construct a structured block-monomial subgroup of coordinate permutations. Several explicit examples show how to generate these codes from first principles without relying on numerical searches. An appendix extends the analysis to BCH-based product constructions. Subjects: Quantum Physics (quant-ph) ; Information Theory (cs.IT) Cite as: arXiv:2608.27565 [quant-ph] (or arXiv:2608.27565v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.27565 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Eric Sabo [ view email ] [v1] Thu, 27 Aug 2026 18:00:04 UTC (86 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2026-08 Change to browse by: cs cs.IT math math.IT References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation 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)

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