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A binary poset code of codimension m (of cardinality 2n-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.

ieee transactions on information theory

The Poset Metrics That Allow Binary Codes of Codimension <formula formulatype="inline"> <tex>$m$</tex></formula> to be <formula formulatype="inline"><tex>$m$</tex> </formula>-, <formula formulatype="inline"><tex>$(m-1)$</tex></formula>-, or <formula formulatype="inline"><tex>$(m-2)$</tex></formula>-Perfect

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