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

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2 Author(s)
Hyun Kwang Kim ; Dept. of Math., Pohang Univ. of Sci. & Technol., Pohang ; Denis S. Krotov

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.

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IEEE Transactions on Information Theory  (Volume:54 ,  Issue: 11 )