On perfect poset codes

Abstract

We consider on F n q metrics determined by posets and classify the parameters of 1-perfect poset codes in such metrics. We show that a code with same parameters of a 1-perfect poset code is not necessarily perfect, however, we give necessary and sufficient conditions for this to be true. Furthermore, we characterize the unique way up to a labeling on the poset, considering some conditions, to extend an r-perfect poset code over F n q to an r-perfect poset code over F n+m q .