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A new upper bound for $A(19,6,8)$

  • Jiang Chang
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Abstract

We compute Polak's bound A4(19,6,8) for binary constant weight codes, obtaining the numerical value $673.04001$. An exact rational certificate gives A4(19,6,8)≤ 673.0400143064802474039375132665301315202504, and hence A(19,6,8)≤ 673. This improves the upper bound $693$ listed in Brouwer's table. The certificate is verified by a separate program using exact rational arithmetic.

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Cite

BibTeXRIS
BibTeX
@misc{chang2026upper,
  title = {{A new upper bound for $A(19,6,8)$}},
  author = {Jiang Chang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00173},
  eprint = {2611.00173},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00173},
}
RIS
TY  - UNPB
TI  - A new upper bound for $A(19,6,8)$
AU  - Jiang Chang
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00173
UR  - https://arxiv.org/abs/2611.00173
AB  - We compute Polak's bound A_4(19,6,8) for binary constant weight codes, obtaining the numerical value $673.04001$. An exact rational certificate gives A_4(19,6,8)≤ 673.0400143064802474039375132665301315202504, and hence A(19,6,8)≤ 673. This improves the upper bound $693$ listed in Brouwer's table. The certificate is verified by a separate program using exact rational arithmetic.
ER  -