Quasi-symmetric 2-(28, 12, 11) designs with an automorphism of order 7 |
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| Authors: | Yuan Ding Sheridan Houghten Clement Lam Suzan Smith Larry Thiel Vladimir D. Tonchev |
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| Affiliation: | 1. Centre Interuniversitaire en Calcul Mathématique Algébrique,* Department of Computer Science, Concordia University, Montreal, Québec, Canada;2. Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, USA |
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| Abstract: | All quasi-symmetric 2-(28, 12, 11) designs with an automorphism of order 7 without fixed points or blocks are enumerated. Up to isomorphism, there are exactly 246 such designs. All but four of these designs are embeddable as derived designs in symmetric 2-(64, 28, 12) designs, producing in this way at least 8784 nonisomorphic symmetric 2-(64, 28, 12) designs. The remaining four 2-(28, 12, 11) designs are the first known examples of nonembeddable quasi-symmetric quasi-derived designs. These symmetric 2-(64, 28, 12) designs also produce at least 8784 nonisomorphic quasi-symmetric 2-(36, 16, 12) designs with intersection numbers 6 and 8, including the first known examples of quasi-symmetric 2-(36, 16, 12) designs with a trivial automorphism group. © 1998 John Wiley & Sons, Inc. J Combin Designs 6: 213–223, 1998 |
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| Keywords: | symmetric design quasi-symmetric design residual design derived design linear code |
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