PreprintarXiv licencearXiv
Optimal self-orthogonal binary linear codes
Abstract
We complete the determination of the minimum possible length of eight-dimensional binary self-orthogonal codes with given minimum distance. For dimension nine we give exact values and bounds for minimum distance at most $64$. By exploiting the geometric reformulation of linear codes as multisets of points, we fully redo the classification for dimension at most seven in a simplified and computer-free manner. As a by-product we prove the non-existence of [93,9,44]2 codes and show several divisibility results for putative optimal nine-dimensional binary codes.
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BibTeX
@misc{kurz2026optimal,
title = {{Optimal self-orthogonal binary linear codes}},
author = {Sascha Kurz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39870},
eprint = {2610.39870},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39870},
}
RIS
TY - UNPB
TI - Optimal self-orthogonal binary linear codes
AU - Sascha Kurz
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39870
UR - https://arxiv.org/abs/2610.39870
AB - We complete the determination of the minimum possible length of eight-dimensional binary self-orthogonal codes with given minimum distance. For dimension nine we give exact values and bounds for minimum distance at most $64$. By exploiting the geometric reformulation of linear codes as multisets of points, we fully redo the classification for dimension at most seven in a simplified and computer-free manner. As a by-product we prove the non-existence of [93,9,44]_2 codes and show several divisibility results for putative optimal nine-dimensional binary codes.
ER -