CSS codes from the Bruhat order of Coxeter groups

Quantum Physics [Submitted on 17 Mar 2026] CSS codes from the Bruhat order of Coxeter groups Kamil Bradler I introduce a method to generate families of CSS codes with interesting code parameters. The object of study is Coxeter groups, both finite and infinite (reducible or not), and a geometrically motivated partial order of Coxeter group elements named after Bruhat. The Bruhat order is known to provide a link to algebraic topology -- it doubles as a face poset capturing the inclusion relations of the p-dimensional cells of a regular CW~complex and that is what makes it interesting for QEC code design. Assisted by the Bruhat face poset interval structure unique to Coxeter groups I show that the corresponding chain complexes can be turned into multitudes of CSS codes. Depending on the approach, I obtain CSS codes (and their families) with controlled stabilizer weights, for example [6006, 924, \{{\leq14},{\leq7}\}] (stabilizer weights~14 and 9) and [22880,3432,\{{\leq8},{\leq16}\}] (weights 16 and 10), and CSS codes with highly irregular stabilizer weight distributions such as [571,199,\{5,5\}]. For the latter, I develop a weight-reduction method to deal with rare heavy stabilizers. Finally, I show how to extract four-term (length three) chain complexes that can be interpreted as CSS codes with a metacheck. Subjects: Quantum Physics (quant-ph); Information Theory (cs.IT); Mathematical Physics (math-ph) Cite as: arXiv:2603.16036 [quant-ph]   (or arXiv:2603.16036v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.16036 Focus to learn more Submission history From: Kamil Bradler [view email] [v1] Tue, 17 Mar 2026 00:43:51 UTC (579 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.IT math math-ph math.IT math.MP References & Citations INSPIRE HEP NASA ADS 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)