On non-connected pointed Hopf algebras of dimension 16 in characteristic 2

Let k be an algebraically closed field. We give a complete classification of non-connected pointed Hopf algebras of dimension 16 with char k = 2 that are generated by grouplike elements and skew-primitive elements. It turns out that there are infinitely many classes (up to isomorphism) of pointed Hopf algebras of dimension 16. In particular, we obtain infinitely many new examples of non- commutative non-cocommutative finite-dimensional pointed Hopf algebras.