Searching for a binary Type II [72,36,16] self-dual code — an open,
community-verifiable search to decide whether this code exists.
- Find it, and we get the next extremal binary Type II code after the
length-24 Golay and length-48 quadratic-residue codes, with a forced weight
enumerator (
A_16 = 249849), a5-(72,16,78)design, a code CFT at central chargec = 36, and a[[71,1,≥15]]self-dual CSS code. - Rule it out, and we settle a question open since Sloane raised it in 1973.
The site makes the problem legible and the eliminations checkable: every proof-grade kill ships an exact, independently re-runnable certificate.
132 length-40 residual candidates → 60 eliminated (proof-grade) → 72
surviving; of those, 51 are witnessed nonempty and 21 are unresolved
(not yet exhausted — not evidence of emptiness). All 8 proof-grade kills are
reproducible in pure Python with no solver.
Requirements: Python 3.10+, pandoc, and PyYAML.
pip install -r requirements.txt
sudo apt-get install -y pandoc # or: brew install pandoc
python build_site.py # render content/ -> HTML, regenerate data/*.json, package repro bundles
python -m http.server 8000 # http://127.0.0.1:8000/The site is base-path safe (a per-page <base> tag is auto-detected), so it
works at a domain root or a project sub-path like /extremal72/.
This repository's CI workflow builds, verifies, link-checks, and deploys the
static site to GitHub Pages on every push to main.
The workflow asks GitHub to enable Pages automatically. If the first deploy is
blocked by repository or organization settings, go to Settings -> Pages and
set Build and deployment -> Source to GitHub Actions, then re-run the
workflow. The site will publish at https://valbert4.github.io/selfdual_site/
unless the repository is renamed or a custom domain is configured.
python repro/verify_all.py # exact-replayable bundles, pure Python, no solver
python check_links.py # internal-link checkEach test ships a reproduction bundle under repro/. The 🟢 bundles cover all
8 proof-grade kills plus the menu re-enumeration, each backed by an exact
Farkas/Smith certificate, an exact bound, or an exhaustive witness.
| Path | What |
|---|---|
index.html, prototype/ |
the dashboard (tabbed UI + styles + tabs.js) |
content/ |
Markdown pages (rendered to HTML by build_site.py) |
data/ |
structured sources of truth (*.yml); the build emits matching *.json |
repro/ |
per-test reproduction bundles + verify_all.py |
downloads/ |
self-contained enumerator / genus-3 / triweight data and bundles |
build_site.py, check_links.py |
the static build and link checker |
Edit the YAML/Markdown sources, not the generated JSON/HTML.
See CONTRIBUTING.md. Discussion happens in the #extremal72 channel of the Error Correction Zoo Discord: https://discord.gg/gg3pJZNYxQ.
Code is under the MIT License; prose and data are additionally offered under CC-BY-4.0. If you use the project or its certificates, please cite it (see CITATION.cff).