Abstract
By using the cogredience theories of an alternate matrix, a symmetric matrix and a Hermitian-symmetric matrix, we will find a special family of generator matrices for any linear code, and then using the special family of generator matrices, we will provide a general method to construct a linear complementary dual (LCD) code (resp. a Hermitian LCD code) from any given linear code. Still using the special family of generator matrices for LCD codes (resp. Hermitian LCD codes), we will present the enumeration of all [n,k] LCD codes (resp. Hermitian LCD codes).
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