Superinfix codes, p-superinfix codes and s-superinfix codes have been introduced and considered by D. L. Van, P. T. Huy and the author in earlier papers. The embedding problem for these classes of codes has been proved to have positive solution in both the finite and regular case. Also, these kinds of codes can be characterized by means of variants of Parikh vectors. In this paper we consider these codes in the case of two-letter alphabets. Based on the mentioned above vector characterizations, it is shown that, for each of the classes of codes under consideration, there exists a procedure to generate all finite maximal codes in the class, starting from anyone among them. Embedding algorithms, other than those obtained earlier, for these classes of codes are also exhibited.