Binary extended perfect codes of length 16 and rank 14
Victor A. Zinoviev, D. V. Zinoviev · Problems of Information Transmission · 2006
All extended binary perfect (16, 4, 2 11 ) codes of rank 14 over the field 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 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 F 2 .