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Linear complementary dual (LCD) codes are linear codes that intersect withtheir dual codes trivially. We study the largest minimum weight $d_2(n,k)$among all binary LCD $[n,k]$ codes and the largest minimum weight $d_3(n,k)$among all ternary LCD $[n,k]$ codes. The largest minimum weights $d_2(n,5)$ and$d_3(n,4)$ are partially determined. We also determine the largest minimumweights $d_2(n,n-5)$, $d_3(n,n-i)$ for $i \in \{2,3,4\}$, and $d_3(n,k)$ for $n\in \{11,12,\ldots,19\}$.

On the minimum weights of binary LCD codes and ternary LCD codes