Hulls of cyclic and negacyclic codes over finite fields

We study the hulls of cyclic and negacyclic codes of length n   over a finite field FqFq with respect to the Euclidean and Hermitian inner products. Based on the characterization of their generator polynomials, the dimensions of the hulls of cyclic and negacyclic codes of length n   over FqFq are determined. The enumerations of cyclic codes and negacyclic codes of length n   over FqFq having hulls of a given dimension are established as well. As special cases, known results concerning complementary dual and self-dual cyclic codes can be viewed as corollaries of results in this paper.