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We study one generator quasi-cyclic codes and four-circulant codes, which arealso quasi-cyclic but have two generators. We state the hull dimensions forboth classes of codes in terms of the polynomials in their generating elements.We prove results such as the hull dimension of a four-circulant code is evenand one-dimensional hull for double-circulant codes, which are special onegenerator codes, is not possible when the alphabet size $q$ is congruent to 3mod 4. We also characterize linear complementary pairs among both classes ofcodes. Computational results on the code families in consideration are providedas well.

On the hull and complementarity of one generator quasi-cyclic codes and four-circulant codes