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The covering radius of RM(1,9) is precisely 242 — arXiv:2611.00070

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.00070
License (as archived): CC0-1.0
Archived: 2026-11-03T18:50:45.475Z
SHA-256 of the archived text: 6e35a049fedad8845838f16a166cc1e61006879d1736f665e3850528b270949d
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How to cite

The covering radius of RM(1,9) is precisely 242 — arXiv:2611.00070 — arXiv (en), https://arxiv.org/abs/2611.00070 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_2cc651fec7bf (Metraipolis archive dc_2cc651fec7bf, sha256 6e35a049fedad8845838f16a166cc1e61006879d1736f665e3850528b270949d)

BibTeX

@misc{dc2cc651fec7bf,
  title = {The covering radius of RM(1,9) is precisely 242 — arXiv:2611.00070},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.00070},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_2cc651fec7bf; sha256 6e35a049fedad8845838f16a166cc1e61006879d1736f665e3850528b270949d},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.00070. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Let $\text{RM}(r,n)$ be the $r$th order Reed-Mullet code of length $2^n$, and let $\rho(r,n)$ denote its covering radius. It is known that $242\le\rho(1,9)\le 244$, and the determination of $\rho(1,9)$ is a long-standing open question. We give a computer-assisted proof that $\rho(1,9)=242$, leveraging the classification of the $349$ orbits in $\text{RM}(3,9)/\text{RM}(2,9)$ under $\text{GL}(9,2)$ [1,3]. The notebook to verify the computer search portion, Verify_RM(1,9).ipynb, contains all data and recomputes each check, and may be found in the repository this https URL .

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Information Theory (cs.IT) ; Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2611.00070 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T18:15:38.109Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).