Codes over F_q^mF{_q{^m}} that are closed under addition, and multiplication with elements from F_q are called F_q-linear codes over F_q^mF_{q{^m}} . For mF_q^mF_{q{^m}} The class of F_q LC codes includes as special cases (i) group cyclic codes over elementary abelian groups (q=p, a prime), (ii) subspace subcodes of Reed–Solomon codes (n=q^m–1) studied by Hattori, McEliece and Solomon, (iii) linear cyclic codes over F_q (m=1) and (iv) twisted BCH codes. Moreover, with respect to any particular F_q-basis of F_q^mF_{q{^m}} , any F_qLC code over F_q^mF_{q{^m}} can be viewed as an m-quasi-cyclic code of length mn over F_q. In this correspondence, we obtain transform domain characterization of F_q LC codes, using Discrete Fourier Transform (DFT) over an extension field of F_q^mF_{q{^m}} The characterization is in terms of any decomposition of the code into certain subcodes and linearized polynomials over F_q^mF_{q{^m}} . We show how one can use this transform domain characterization to obtain a minimum distance bound for the corresponding quasi-cyclic code. We also prove nonexistence of self dual F_q LC codes and self dual quasi-cyclic codes of certain parameters using the transform domain characterization.