  Linear complementary dual (LCD) codes are linear codes which intersect their
dual codes trivially, which have been of interest and extensively studied due
to their practical applications in computational complexity and information
protection. In this paper, we give some methods for constructing LCD codes over
small finite fields by modifying some typical methods for constructing linear
codes. We show that all odd-like binary LCD codes, ternary LCD codes and
quaternary Hermitian LCD codes can be constructed using the modified methods.
Our results improve the known lower bounds on the largest minimum distances of
LCD codes. Furthermore, we give two counterexamples to disprove the conjecture
proposed by Bouyuklieva (Des. Codes Cryptogr. 89(11): 2445-2461, 2021).
