Construction of quaternary Hermitian LCD codes

We introduce a general construction of many Hermitian LCD $[n,k]$ codes from a given Hermitian LCD $[n,k]$ code. Furthermore, we present some results on punctured codes and shortened codes of quaternary Hermitian LCD codes. As an application, we improve some of the previously known lower bounds on the largest minimum weights of quaternary Hermitian LCD codes of length $12\le n\le 30$.