发表机构
MIGAL – Galilee Research Institute; Tel-Hai University of Kiryat Shmona in the Galilee（MIGAL加利利研究所; 加利利基里亚特谢莫纳泰尔海大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究精确确定了长度为$2^m-1$的二元本原三重纠错BCH码$\text{BCH}(3,m)$的第二广义覆盖半径为8（对所有$m\not\neq5$），匹配已知下界，解决了该码族的该参数确定问题。
AI 中文摘要
设$C_m=\text{BCH}(3,m)$为长度$2^m-1$的二元本原三重纠错BCH码。我们精确确定了它的第二广义覆盖半径：对所有$m\neq5$，$R_2(C_m)=8$。等价地，每个二维伴随子空间都包含在至多8个奇偶校验列的二元张成中，且最坏情况下需要8列。这一结果与已知下界相符，确定了整个二元本原三重纠错BCH码族的该参数。
英文摘要
Let $C_m:=\mathrm{BCH}(3,m)$ be the binary primitive triple-error-correcting BCH code of length $2^m-1$. We determine its second generalized covering radius exactly: $R_2(C_m)=8$ for every $m\geq5$. Equivalently, every two-dimensional syndrome subspace is contained in the binary span of at most eight parity-check columns, and eight columns are necessary in the worst case. This matches the known lower bound.
Comments25 pages. Revised proofs and exposition; main result unchanged. The accompanying verification artifact is available at https://doi.org/10.5281/zenodo.21796632
