Some bounds on binary LCD codes

초록

A linear code with a complementary dual (or An LCD code) is defined to be a linear code C whose dual code C-perpendicular to satisfies C boolean AND C-perpendicular to={0}. Let LD(n, k) denote the maximum of possible values of d among [n, k, d] binary LCD codes. We give the exact values of LD(n, k) for k = 2 for all n and some bounds on LD(n, k) for other cases. From our results and some direct search we obtain a complete table for the exact values of LD(n, k) for 1 <= k <= n <= 12. As a consequence, we also derive bounds on the dimensions of LCD codes with fixed lengths and minimum distances.

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