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On the maximum cocliques of the rank 3 graph of 211 : M24

✍ Scribed by Naoyuki Horiguchi; Masaaki Kitazume; Hiroyuki Nakasora

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
126 KB
Volume
17
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

In this article, we consider the maximum cocliques of the 2^11^: M~24~ ‐graph Ξ›. We show that the maximum cocliques of size 24 of Ξ› can be obtained from two Hadamard matrices of size 24, and that there are exactly two maximum cocliques up to equivalence. We verify that the two nonisomorphic designs with parameters 5‐(24,9,6) can be constructed from the maximum cocliques of Ξ›, and that these designs are isomorphic to the support designs of minimum weights of the ternary extended quadratic residue and Pless symmetry [24,12,9] codes. Further, we give a new construction of Ξ› from these 5‐(24,9,6) designs. Β© 2009 Wiley Periodicals, Inc. J Combin Designs 17: 323–332, 2009

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