RM(1,9) covering radius = 242, three proofs
Awaiting review
The takeaway
The maximum nonlinearity of a Boolean function in nine variables, equivalently the covering radius of RM(1,9), was known only to lie between 242 and 244.
Status
- Claim
Awaiting review
- Our reporting
- Medium confidence
- Verification
- Preprint only
- Importance
- 3 of 5
- Last verified
- 3 November 2026
Your AI and this story
- GPT-6 Astra187 days after its cutoff
- Claude Opus 5.5126 days after its cutoff
- Gemini 4 Argon217 days after its cutoff
- Grok 4.7156 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 126 days before it.
Key facts
- Previously known: 242 ≤ ρ(1,9) ≤ 244; for odd n, ρ(1,n) was known only for n ≤ 7 (Hou–Sabo–Slaughter abstract)
- Hou–Sabo–Slaughter: a function of nonlinearity 243 yields one of 244; 244 excluded through Walsh-spectrum divisibility and an exhaustive search over the 349 GL(9,2)-orbits of RM(3,9)/RM(2,9), run twice with independent implementations; code at github.com/FreemanSlaughter/Covering-Radius
- Yi Li (2611.00890): one-point rigidity theorem plus spectral and computational exclusion of 243 and 244. Acknowledgment (verbatim): ‘The author acknowledges the use of ChatGPT (OpenAI) in the research and preparation of this paper, including mathematical discussions, exposition, LaTeX editing, and assistance with computational code.’
- Verification status: three unrefereed computer-assisted preprints reaching the same value
What happened
A long-standing question in Boolean-function cryptography received three proofs: one in mid-October with no AI statement, and two more on arXiv this week, one of which used ChatGPT for discussions and code.
Why it matters
Nonlinearity bounds matter for cipher design; agreement between three independent computer-assisted proofs makes the value 242 more credible. The AI role is a minor one; the entry mainly records the convergence.
What is disputed or not yet verified
| Verification | Three independent preprints, computer-assisted |
|---|
Sources
4 sources from 2 sites. Numbers match the chips in the text.
4 sources: 4 primary
Primary
- arXiv 2611.00890: The covering radius of RM(1,9) is 242 (Yi Li)arxiv.org, paper
- IACR ePrint 2026/2529: The Covering Radius of RM(1,9) is Precisely 242 (Hou, Sabo, Slaughter)eprint.iacr.org, paper
- arXiv 2611.00070 (Hou, Sabo, Slaughter)arxiv.org, paper
- arXiv 2610.17871 (Wang, Lou et al.)arxiv.org, paper
Changes
- Filed. Resolves the 14 Oct lead on 2610.17871