LAUSR

In this paper, we show that LCD codes are not equivalent to non-LCD codes over small finite fields. The enumeration of binary optimal LCD codes is obtained. We also get the exact value of LD( n ,2) over F 3 $\mathbb {F}_{3}$ and F 4 $\mathbb {F}_{4}$ , where LD( n ,2) := m a x { d ∣ t h e r e e x s i t s a n [ n ,2, d ] LCD c o d e o v e r F q } $ code~ over~ \mathbb {F}_{q}\}$ . We study the bound of LCD codes over F q $\mathbb {F}_{q}$ and generalize a conjecture proposed by Galvez et al. about the minimum distance of binary LCD codes.