arXiv:2610.39870 · v1

Optimal self-orthogonal binary linear codes

首次提交 2026-10-29 19:44

版本更新 2026-10-29 19:44

雷达观测 2026-10-30 13:28

摘要

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.

作者备注：39 pages; comments more than welcome