TY - JOUR

T1 - The cardinality of some symmetric differences

AU - Huang, Po Yi

AU - Ke, Wen Fong

AU - Pilz, Günter F.

N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.

PY - 2010/3

Y1 - 2010/3

N2 - In this paper, we prove that for positive integers k and n, the cardinality of the symmetric differences of {1, 2,. . ., k}, {2, 4,. . ., 2k}, {3, 6,. . ., 3k},. . ., {n, 2n,. . ., kn} is at least k or n, whichever is larger. This solved a problem raised by Pilz in which binary composition codes were studied.

AB - In this paper, we prove that for positive integers k and n, the cardinality of the symmetric differences of {1, 2,. . ., k}, {2, 4,. . ., 2k}, {3, 6,. . ., 3k},. . ., {n, 2n,. . ., kn} is at least k or n, whichever is larger. This solved a problem raised by Pilz in which binary composition codes were studied.

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U2 - 10.1090/S0002-9939-09-10189-2

DO - 10.1090/S0002-9939-09-10189-2

M3 - Article

AN - SCOPUS:77951496298

VL - 138

SP - 787

EP - 797

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 3

ER -