Characterization of extended Hamming and Golay codes as perfect codes in poset block spaces

B. K. Dass, Namita Sharma, Rashmi Verma
2018 Advances in Mathematics of Communications  
Alves, Panek and Firer (Error-block codes and poset metrics, Adv. Math. Commun., 2 (2008), 95-111) classified all poset block structures which turn the [8, 4, 4] extended binary Hamming code into a 1-perfect poset block code. However, the proof needs corrections that are supplied in this paper. We provide a counterexample to show that the extended binary Golay code is not 1-perfect for the proposed poset block structures. All poset block structures turning the extended binary and ternary Golay
more » ... odes into 1-perfect codes are classified. 2010 Mathematics Subject Classification: Primary: 94B05; Secondary: 94B60.
doi:10.3934/amc.2018037 fatcat:6thmiawbfnajjnmayogyyvxvee