  In this paper, we give a new method for constructing LCD codes. We employ
group rings and a well known map that sends group ring elements to a subring of
the $n \times n$ matrices to obtain LCD codes. Our construction method
guarantees that our LCD codes are also group codes, namely, the codes are
ideals in a group ring. We show that with a certain condition on the group ring
element $v,$ one can construct non-trivial group LCD codes. Moreover, we also
show that by adding more constraints on the group ring element $v,$ one can
construct group LCD codes that are reversible. We present many examples of
binary group LCD codes of which some are optimal and group reversible LCD codes
with different parameters.
