A group extensions approach to relative difference sets

Journal of Combinatorial Designs

Volumn 12, Issue 4, 2004, Pages 279-298

  Galati, John C ^a  

^a RMIT UNIVERSITY   (Australia)

Author keywords

Divisible design; Generalized Hadamard matrix; Non abelian relative difference set; Relative difference set

Indexed keywords

EID: 3042549701     PISSN: 10638539     EISSN: 15206610     Source Type: Journal    
DOI: 10.1002/jcd.10090     Document Type: Article

References (24)

1. J. L. Alperin and R. B. Bell, Groups and Representations, Springer, New York, 1995.
2. K. T. Arasu, J. F. Dillon, D. Jungnickel, and A. Pott, The solution of the Waterloo Problem, J Combin Theory Ser A 71 (1995), 316-331.
3. K. T. Arasu, J. F. Dillon, K. H. Leung, and S. L. Ma, Cyclic relative difference sets with classical parameters, J Combin Theory Ser A 94 (1) (2001), 118-126. (Pubitemid 33380994)
4. K. T. Arasu, D. Jungnickel, S. L. Ma, and A. Pott, Relative difference sets with n = 2, Discrete Math 147 (1995), 1-17.
5. T. Beth, D. Jungnickel, and H. Lenz, Design Theory. Vol. 1 (2nd edn.), Cambridge University Press, Cambridge, 1999.
6. C. J. Colbourn and J. H. Dinitz (Eds.), The CRC Handbook of Combinatorial Designs, CRC Press, Boca Raton, 1996.
7. P. Dembowski and F. Piper, Quasiregular collineation groups of finite projective planes, Math Z 99 (1967), 53-75.
8. J. E. H. Elliott and A. T. Butson, Relative difference sets, Illinois J Math 10 (1966), 517-531.
9. D. L. Flannery, Cocyclic Hadamard matrices and Hadamard groups are equivalent, J Algebra 192 (1997), 749-779. (Pubitemid 127170594)
10. J. C. Galati, Application of Gaschütz' Theorem to relative difference sets in non-abelian groups, J Combin Des 11 (2003), 307-311.
11. J. C. Galati, A group extensions approach to relative difference sets, Ph.D. Thesis, RMIT University, Melbourne, Australia, 2003.
12. M. J. Ganley and E. Spence, Relative difference sets and quasiregular collineation groups, J Combin Theory Ser A 19 (1975), 134-153.
13. Y. Hiramine, Affine difference sets and related factor sets, Geom Dedicata 54 (1995), 13-29.
14. Y. Hiramine, Factor sets associated with regular collineation groups, J Algebra 142 (1991), 414-423.
15. K. J. Horadam, Equivalence classes of central semiregular relative difference sets, J Combin Des 8 (2000), 330-346.
16. K. J. Horadam, An introduction to cocyclic generalized Hadamard matrices, Discrete Appl Math 102 (2000), 115-131.
17. G. Hughes, Characteristic functions of relative difference sets, correlated sequences and Hadamard matrices, In: M. Fossorier et al. (Eds.), AAECC-13, Lecture notes in computer science, Vol. 1719, Springer, Berlin, 1999, pp. 346-354.
18. D. L. Johnson, Presentations of Groups, (2nd edn)., London Mathematical Society Student Texts, Vol. 15, Cambridge University Press, Cambridge, 1997.
19. D. Jungnickel, On automorphism groups of divisible designs, Canad J Math 34 (1982), 257-297.
20. W. H. Liu, Central semiregular relative difference sets fixed by inversion, Ph.D. Thesis, RMIT University, Melbourne, Australia, 2002.
21. A. A. I. Perera and K. J. Horadam, Cocyclic generalized Hadamard matrices and central relative difference sets, Des Codes Cryptogr 15 (1998), 187-200. (Pubitemid 128508042)
22. A. Pott, Finite geometry and character theory, Springer, Berlin, 1995.
23. A. Pott, A survey on relative difference sets'', In: Groups, difference sets, and the monster, proceedings of a special research quarter at the Ohio State University, Walter de Gruyter, Berlin, 1996.
24. D. J. S. Robinson, A Course in the theory of groups (2nd edn.), Springer, New York, 1996.