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

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

2007-05-19

arxiv.org/abs/0705.2807v2

IEEE Trans. Inf. Theory 54(11) 2008, 5241-5246

Mathematics

Combinatorics

6pp, 33fig. V2: revised

Scientific paper

10.1109/TIT.2008.929972

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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