The poset metrics that allow binary codes of codimension m to be m-, (m-1)-, or (m-2)-perfect
Combinatorics
2008-10-26 v2 Discrete Mathematics
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 disjoin chains. Index terms: perfect codes, poset codes
Cite
@article{arxiv.0705.2807,
title = {The poset metrics that allow binary codes of codimension m to be m-, (m-1)-, or (m-2)-perfect},
author = {Hyun Kwang Kim and Denis Krotov},
journal= {arXiv preprint arXiv:0705.2807},
year = {2008}
}
Comments
6pp, 33fig. V2: revised