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# An Upper Bound for the Cardinality of an s-Distance Set in Euclidean Space

Author:
Etsuko Bannai   Kazuki Kawasaki   Yusuke Nitamizu and Teppei Sato

Journal:
Combinatorica

Issue Date:
2003

Abstract(summary):

In this paper we show that if X is an s-distance set in${\left| X \right|} \leqslant {\sum\nolimits_{i = 0}^{2p - 1} {{\left( {{*{20}c} {{m + s - i - 1}} \\ {{s - i}} \\ } \right)}} }$ {\left| X \right|} \leqslant {\sum\nolimits_{i = 0}^{2p - 1} {{\left( {\begin{array}{*{20}c} {{m + s - i - 1}} \\ {{s - i}} \\ \end{array} } \right)}} } Moreover ifX is antipodal, then ${\left| X \right|} \leqslant 2{\sum\nolimits_{i = 0}^{p - 1} {{\left( {{*{20}c} {{m + s - 2i - 2}} \\ {{m - 1}} \\ } \right)}} }$ {\left| X \right|} \leqslant 2{\sum\nolimits_{i = 0}^{p - 1} {{\left( {\begin{array}{*{20}c} {{m + s - 2i - 2}} \\ {{m - 1}} \\ \end{array} } \right)}} } .

Page:
535-557

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