Structure and automorphism groups of Hadamard designs
Eric Merchant
On Time Systems Inc. 1850 Millrace Dr., Suite 1 Eugene OR 97403 USA 1850 Millrace Dr., Suite 1 Eugene OR 97403 USA
DOI: 10.1007/s10801-006-0012-9
Abstract
Let n be the order of a Hadamard design, and G any finite group. Then there exists many non-isomorphic Hadamard designs of order 2 12|G| + 13 n with automorphism group isomorphic to G.
Pages: 137–155
Keywords: keywords Hadamard designs; automorphisms of designs
Full Text: PDF
References
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2. T. Beth, D. Jungnickel, and H. Lenz, Design Theory, Cambridge University Press, Cambridge, 1999.
3. U. Dempwolff and W.M. Kantor, Distorting symmetric designs. in preparation
4. D. Jungnickel, “The number of designs with classical parameters grows exponentially,” Geometriae Dedicata 16 (1984), 167-178.
5. W.M. Kantor, “Characterizations of finite projective and affine spaces,” Can. J. Math. 21 (1969), 64-75.
6. W.M. Kantor, “Automorphism Groups of Hadamard Matrices,” J. Comb. Theory 6 (1969), 279-281.
7. W.M. Kantor, “Automorphisms and isomorphisms of symmetric and affine designs,” J. Alg. Comb. 3 (1994), 301-338.
8. W.M. Kantor, “Note on GMW designs,” Europ. J. Comb. (22) (2001), 63-69.
9. W.M. Kantor, unpublished manuscript.
10. M.E. Kimberley, “On the construction of certain Hadamard designs,” Math Z. 119 (1971), 41-59.
11. C. Lam, S. Lam, and V.D. Tonchev, “Bounds on the number of Hadamard designs of even order,” J. Comb. Designs 9 (2001), 363-378.
12. E. Merchant, “Exponentially many Hadamard designs,” Des. Codes. and Cryptogr. 38(2) (2006), 297- 308.
13. C.W. Norman, “Hadamard designs with no non-trivial automorphisms,” Geom. Ded. 2 (1976), 201-204.
14. C.W. Norman, “Non-isomorphic Hadamard designs,” J. Combin. Theory (A) 21 (1976), 336-344.
15. R.E.A.C. Paley, “On Orthogonal Matrices,” J. Math. Phys. 12 (1933), 311-320.
16. O. Pfaff, “The classification of doubly transitive affine designs,” Des., Codes, Cryptogr. 1 (1991), 207-217.
17. D.E. Taylor, The Geometry of the Classical Groups, Heldermann Verlag, Berlin, 1992.
18. J.A. Todd, “A combinatorial problem,” J. Math. Phys. 12 (1933), 321-333.