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Covering 1024 syndromes with 50 columns
We exhibit a binary linear $[50,40]_2$ code of covering radius $2$, so $\ell_2(10,2)\le 50$, one column below the Kaikkonen--Rosendahl length $51$ that has stood since 2003 and that still seeds the $R=2$ family of Davydov--Marcugini--Pambianco (arXiv:2511.02542). The new matrix admits a $(2,0)$-part
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