Binary Extended Perfect Codes of Length 16 and Rank 14

All extended binary perfect $(16,4,2^11)$ codes of rank 14 over the field $\mathbb F_2$ are classified. It is proved that among all nonequivalent extended binary perfect $(16,4,2^11)$ codes there are exactly 1719 nonequivalent codes of rank 14 over $\mathbb F_2$. Among these codes there are 844 codes classified by Phelps (Solov?eva–Phelps codes) and 875 other codes obtained by the construction of Etzion–Vardy and by a new general doubling construction, presented in the paper. Thus, the only open question in the classification of extended binary perfect $(16,4,2^11)$ codes is that on such codes of rank 15 over $\mathbb F_2$.