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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Sascha Kurz (2026) studied this question.
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