TY - JOUR
T1 - The cardinality of some symmetric differences
AU - Huang, Po Yi
AU - Ke, Wen Fong
AU - Pilz, Günter F.
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.
UR - http://www.scopus.com/inward/record.url?scp=77951496298&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77951496298&partnerID=8YFLogxK
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 -