The poset structures admitting the extended binary Hamming code to be a perfect code
The authors characterize the partially ordered sets (posets) \(P\) for which an extended binary Hamming code is a double or triple error-correcting perfect code under the poset metric \(d_{P}\). For the two extended Hamming codes such posets are showed explicitly. These results follow and complete a previous work by \textit{R.A. Brualdi}, \textit{J.S. Graves} and \textit{K.M. Lawrence} in [Discrete Math. 147, 57--72 (1995; Zbl 0854.94019)].
scientific article; zbMATH DE number 2127153