  Linear codes with complementary duals are linear codes whose intersection
with their duals are trivial, shortly named LCD codes. In this paper we outline
a construction for LCD codes over finite fields of order $q$ using weighing
matrices and their orbit matrices. The LCD codes constructed can be of any
length dimension according to the choice of matrices used in their
construction. As a special case, LCD codes of length $2n$ and dimension $n$ are
constructed which also have the property of being formally self-dual.
Alternatively, under a condition depending on $q$ that the codes are not LCD,
this method constructs self-dual codes. To illustrate the method we construct
LCD codes from weighing matrices, including the Paley conference matrices and
Hadamard matrices. We also extend the construction to Hermitian LCD codes over
the finite field of order 4. In addition, we propose a decoding algorithm that
can be feasible for the LCD codes obtained from some of the given methods.
