The Existence of a Bush-Type Hadamard Matrix of Order 324 and Two New Infinite Classes of Symmetric Designs

Designs, Codes, and Cryptography

Volumn 24, Issue 2, 2001, Pages 225-232

  Janko, Zvonimir ^a   Kharaghani, Hadi ^b   Tonchev, Vladimir D ^c  

^a UNIVERSITY OF HEIDELBERG   (Germany)

^b UNIVERSITY OF LETHBRIDGE   (Canada)

^c MICHIGAN TECHNOLOGICAL UNIVERSITY   (United States)

Author keywords

Balanced generalized weighing matrix; Bush type Hadamard matrix; Mutually orthogonal Latin squares; Projective plane; Strongly regular graph; Symmetric design

Indexed keywords

EID: 0035479587     PISSN: 09251022     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1011212922844     Document Type: Article

References (12)

1. T. Beth, D. Jungnickel and H. Lenz, Design Theory, 2nd ed., Cambridge University Press, Cambridge (1999).
2. K. A. Bush, Unbalanced Hadamard matrices and finite projective planes of even order, J. Combin. Theory Vol. 11 (1971) pp. 38-44.
3. F. C. Bussemaker, W. Haemers and E. Spence, The search for pseudo orthogonal Latin squares of order six, Designs, Codes and Cryptography Vol. 9 (2001) pp. 72-78.
4. D. R. Hughes and F. C. Piper, Design Theory, Cambridge University Press, Cambridge (1985).
5. W. H. Haemers and V. D. Tonchev, Spreads in strongly regular graphs, Designs, Codes and Cryptography, Vol. 8 (1996) pp. 145-157.
6. Y. J. Ionin, New symmetric designs from regular Hadamard matrices, Electronic J. Combinatorics, Vol. 5 No. R1 (1998).
7. Z. Janko, Coset enumeration in groups and constructions of symmetric designs, Combinatorics, Vol. 90 (1992) pp. 275-277.
8. Z. Janko, H. Kharaghani and V. D. Tonchev, Bush-type Hadamard matrices and symmetric designs, J. Combinatorial Designs, Vol. 9 (2001) pp. 72-78.
9. D. Jungnickel and V. Tonchev, Perfect Codes and Balanced Weighing Matrices, Finite Fields and Their Applications, Vol. 5 (1999) pp. 294-300.
10. H. Kharaghani, New classes of weighing matrices, Ars Combinatoria, Vol. 19 (1985) pp. 69-72.
11. H. Kharaghani, On the twin designs with the lonin-type parameters, The Electronic Journal of Combinatorics, Vol. 7, No. R1 (2000).
12. W. D. Wallis, On a problem of K. A. Bush, Bull. Austral. Math. Soc., Vol. 6 (1972) pp. 321-326.