On the maximum cocliques of the rank 3 graph of 211 : M24 |
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Authors: | Naoyuki Horiguchi Masaaki Kitazume Hiroyuki Nakasora |
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Institution: | 1. Graduate School of Science, Chiba University, Chiba 263‐8522, Japan;2. Department of Mathematics and Informatics, Chiba University, Chiba 263‐8522, Japan;3. Graduate School of Natural Science and Technology Okayama University, Okayama 700‐8530, Japan |
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Abstract: | In this article, we consider the maximum cocliques of the 211: M24 ‐graph Λ. We show that the maximum cocliques of size 24 of Λ 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 Λ, 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 Λ from these 5‐(24,9,6) designs. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 323–332, 2009 |
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Keywords: | strongly regular graphs t‐designs codes Hadamard matrices sporadic simple groups |
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