The Poset Metrics That Allow Binary Codes of Codimension m to be m-, (m-1)-, or (m-2)-Perfect

Abstract

A binary poset code of codimension m (of cardinality 2(n - m), where n is the code length) can correct maximum m errors. All possible poset metrics; that allow codes of codimension m to be m-, (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 of r-perfect poset codes for some r in the case of the crown poset and in the case of the union of disjoint chains.