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- W2952792015 abstract "A linear code with a complementary dual (or LCD code) is defined to be a linear code $C$ whose dual code $C^{perp}$ satisfies $C cap C^{perp}$= $left{ mathbf{0}right} $. Let $LCD{[}n,k{]}$ denote the maximum of possible values of $d$ among $[n,k,d]$ binary LCD codes. We give exact values of $LCD{[}n,k{]}$ for $1 le k le n le 12$. We also show that $LCD[n,n-i]=2$ for any $igeq2$ and $ngeq2^{i}$. Furthermore, we show that $LCD[n,k]leq LCD[n,k-1]$ for $k$ odd and $LCD[n,k]leq LCD[n,k-2]$ for $k$ even." @default.
- W2952792015 created "2019-06-27" @default.
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- W2952792015 date "2017-01-15" @default.
- W2952792015 modified "2023-09-25" @default.
- W2952792015 title "Some Bounds on Binary LCD Codes" @default.
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- W2952792015 doi "https://doi.org/10.48550/arxiv.1701.04165" @default.
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