The poset metrics that allow binary codes of codimension m to be m-, (m-1)-, or (m-2)-perfect

Denis Krotov (Sobolev Institute of Mathematics; Hyun Kwang Kim (Pohang University of Science; Novosibirsk; Russia); South Korea); Technology

arxiv: 0705.2807 · v2 · submitted 2007-05-19 · 🧮 math.CO · cs.DM

The poset metrics that allow binary codes of codimension m to be m-, (m-1)-, or (m-2)-perfect

Hyun Kwang Kim (Pohang University of Science , Technology , South Korea) , Denis Krotov (Sobolev Institute of Mathematics , Novosibirsk , Russia) This is my paper

classification 🧮 math.CO cs.DM

keywords posetcodesperfectcodimensionallowbinarycasecode

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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 disjoin chains. Index terms: perfect codes, poset codes

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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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