The Poset Metrics That Allow Binary Codes of Codimension $m$ to be $m$-, $(m-1)$-, or $(m-2)$-Perfect
Hyun Kwang Kim, Denis S. Krotov · IEEE Transactions on Information Theory · 2008
A binary poset code of codimensionm(of cardinality 2n-m, wherenis the code length) can correct maximummerrors. All possible poset metrics that allow codes of codimensionmto bem-, (m-1)-, or (m-2)-perfect are described. Some general conditions on a poset which guarantee the nonexistence of perfect poset codes are derived; as examples, we prove the nonexistence ofr-perfect poset codes for somerin the case of the crown poset and in the case of the union of disjoint chains.