The poset structures admitting the extended binary Golay code to be a perfect code

Brualdi et al. [Codes with a poset metric, Discrete Math. 147 (1995) 57–72] introduced the concept of poset codes, and gave an example of poset structure which admits the extended binary Golay code to be a 4-error-correcting perfect PP-code. In this paper we classify all of the poset structures which admit the extended binary Golay code to be a 4-error-correcting perfect PP-code, and show that there are no posets which admit the extended binary Golay code to be a 5-error-correcting perfect PP-code.