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In this paper, we deal with a characterization of the posets with the property that every poset isometry of Fn q fixing the origin is a linear map. We say such a poset to be admitting the linearity of isometries. We show that a poset P admits the linearity of isometries over Fn q if and only if P is a disjoint sum of chains of cardinality 2 or 1 when q = 2, or P is an anti-chain otherwise.
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참고문헌 (8)
참고문헌 신청
F. J. MacWilliams / 1998 / The Theory of Error-Correcting Codes / North-Holland
H. Fripertinger / 2005 / Enumeration of the semilinear isometry classes of linear codes / Bayreuth. Math. Schr 74 : 100 ~ 122
H. K. Kim / 2008 / The poset metrics that allow binary codes of codimension m to be m-, (m?1)-, or (m?2)-perfect / IEEE Trans. Inform. Theory 54 (11) : 5241 ~ 5246
J. Y. Hyun / 2008 / Maximum distance separable poset codes / Des. Codes Cryp-togr 48 (3) : 247 ~ 261
J. Y. Hyun / 2010 / A subgroup of the full poset-isometry group / SIAM J. Discrete Math 24 (2) : 589 ~ 599
H. Fripertinger / 2005 / Enumeration of the semilinear isometry classes of linear codes / Bayreuth. Math. Schr 74 : 100 ~ 122
H. K. Kim / 2008 / The poset metrics that allow binary codes of codimension m to be m-, (m?1)-, or (m?2)-perfect / IEEE Trans. Inform. Theory 54 (11) : 5241 ~ 5246
J. Y. Hyun / 2008 / Maximum distance separable poset codes / Des. Codes Cryp-togr 48 (3) : 247 ~ 261
J. Y. Hyun / 2010 / A subgroup of the full poset-isometry group / SIAM J. Discrete Math 24 (2) : 589 ~ 599
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