On the largest minimum distances of [n,6] LCD codes

Linear complementary dual (LCD) codes can be used to against side-channel attacks and fault noninvasive attacks. Let dₐ(n,6) and dₗ(n,6) be the minimum weights of all binary optimal linear codes and LCD codes with length n and dimension 6, respectively.In this article, we aim to obtain the values of dₗ(n,6) for n≥ 51 by investigating the nonexistence and constructions of LCD codes with given parameters. Suppose that s ≥ 0 and 0≤ t≤ 62 are two integers and $n=63s+t$. Using the theories of defining vectors, generalized anti-codes, reduced codes and nested codes, we exactly determine dₗ(n,6) for t ∉\21,22,25,26,33,34,37,38,45,46\, while we show that dₗ(n,6)∈\{dₐ(n,6)$ $-1,dₐ(n,6)\}$ for $t∈\{21,22,26,34,37,38,46\}$ and $ dₗ(n,6)∈ₐ(n,6)-2, dₐ(n,6)-1\ fort∈25,33,45\.