LAUSR

A linear code with a complementary dual (or An LCD code) is defined to be a linear code C whose dual code C⊥ satisfies C ∩ C⊥= 0$\left \{ \mathbf {0}\right \} $. 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.