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

Abstract

Brualdi et al. introduced the concept of poset codes, and gave an example of poset structure which admits the extended binary Hamming code to be a double-error-coffecting perfect P-code. Our study is motivated by this example. In this paper we classify all poset structures which admit the extended binary Hamming code to be a double or triple-error-correcting perfect P-code. (C) 2004 Elsevier B.V. All rights reserved.