Abstract
In this paper we present constructions for group divisible designs from generalized partial difference matrices. We describe some classes of examples.
Similar content being viewed by others
References
K. T. Arasu, W. H. Haemers, D. Jungnickel and A. Pott, Matrix constructions of divisible designs, Lin. Algebra and Appl., Vol. 153 (1991) pp. 123–133.
G. Berman, Families of generalized weighing matrices, Can. J. Math., Vol. 30 (1978) pp. 1016–1028.
R. C. Bose and W. S. Connor, Combinatorial properties of group divisible incomplete block designs, Ann. Math. Stat., Vol. 23 (1952) pp. 367–383.
A. T. Butson, Generalized Hadamard matrices, Proc. Amer. Math. Soc., Vol. 13 (1962) pp. 894–898.
P. Delsarte, J. M. Goethals and J. J. Seidel, Orthogonal matrices with zero diagonal II, Can. J. Math., Vol. 23 (1971) pp. 816–832.
J. M. Goethals and J. J. Seidel, Orthogonal matrices with zero diagonal, Can. J. Math., Vol. 19 (1967) pp. 1001–1010.
D. Jungnickel, On difference matrices, resolvable transversal designs and generalized Hadamard matrices, Math. Z., Vol. 167 (1979) pp. 49–60.
D. Jungnickel, On automorphism groups of divisible designs, Canad. J. Math., Vol. 34 (1982) pp. 257–297.
D. Jungnickel, On automorphism groups of divisible designs, II: Group invariant generalized conference matrices, Arch. Math., Vol. 54 (1990) pp. 200–208.
S. Kageyama and T. Tanaka, Some families of group divisible designs, J. Stat. Plann. Inf., Vol. 5 (1981) pp. 231–241.
R. Mathon and A. Rosa, Tables of parameters of BIBD's with r ≤ 41 including existence, enumeration and resolvability results: An update, Ars Combinatoria, Vol. 30 (1990) pp. 65–96.
J. Seberry, A class of group divisible designs, Ars Combinatoria, Vol. 6 (1978) pp. 151–152.
J. Seberry, Some remarks on generalized Hadamard matrices and theorems of Rajkundlia on SBIBDs: Combinatorial mathematics VI, Springer Lecture Notes, Berlin-Heidelberg-New York, 748 (1979) pp. 154–164.
J. Seberry, A construction for generalized Hadamard matrices, J. Stat. Pl. Inf., Vol. 4 (1980) pp. 365–368.
J. Singer, A theorem in finite projective geometry and some applications to number theory, Trans. Amer. Math. Soc., Vol. 43 (1938) pp. 377–385.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Landgev, I.N. Constructions of Group Divisible Designs. Designs, Codes and Cryptography 8, 309–318 (1996). https://doi.org/10.1023/A:1027303807104
Issue Date:
DOI: https://doi.org/10.1023/A:1027303807104