Linear complementary dual (LCD) codes can provide an optimum linear coding solution for the two-user binary adder channel. LCD codes also can be used to against side-channel attacks and fault non-invasive attacks. Let dLCD(n,k) denote the maximum value of d for which a binary [n,k,d] LCD code exists. In \cite{BS21}, Bouyuklieva conjectured that dLCD(n+1,k)=dLCD(n,k) or dLCD(n,k)+1 for any lenth n and dimension k >= 2. In this paper, we first prove Bouyuklieva's conjecture \cite{BS21} by constructing a binary [n,k,d-1] LCD codes from a binary [n+1,k,d] LCDo,e code, when d >= 3 and k >= 2. Then ...
