  The hull of a linear code over finite fields is the intersection of the code
and its dual, which was introduced by Assmus and Key. In this paper, we develop
a method to construct linear codes with trivial hull ( LCD codes) and
one-dimensional hull by employing the positive characteristic analogues of
Gauss sums. These codes are quasi-abelian, and sometimes doubly circulant. Some
sufficient conditions for a linear code to be an LCD code (resp. a linear code
with one-dimensional hull) are presented. It is worth mentioning that we
present a lower bound on the minimum distances of the constructed linear codes.
As an application, using these conditions, we obtain some optimal or almost
optimal LCD codes (resp. linear codes with one-dimensional hull) with respect
to the online Database of Grassl.
