Binary Extended Perfect Codes of Length 16 by the Generalized Concatenated Construction

We enumerate binary extended nonlinear perfect codes of length 16 obtained by the generalized concatenated construction (GC-construction). There are 15 different types of such codes. They are defined by pairs of MDS codes $A_i:(4,2,64)_4$. For every pair, we give the number of nonequivalent codes of this type. In total, there are 285 nonequivalent binary extended nonlinear perfect codes of length 16 obtained by the GC-construction, including the Hamming (i.e., linear) code. Thus, we obtain all binary extended perfect codes of length 16 and rank 13. Their total number is equal to 272.