Abstract
We introduce the method of assigning values in a ring to the points of a t-design. We give the notion of an \(\left[ {A,t} \right]\)-design. We give a generalization of the concept of association scheme, and obtain a method to construct some of them from t-designs that generalizes the well-known construction for the case of ordinary association schemes.
Similar content being viewed by others
References
T. Beth, D. Jungnickel and H. Lenz, Design Theory, Cambridge University Press (1993).
P. J. Cameron, Near-regularity conditions for designs, Geom. Dedicata, Vol. 2 (1973) pp. 213–223.
K. W. Johnson and J. D. H. Smith, Characters of finite quasigroups IV: products and superschemes, Eur. J. Comb., Vol. 10, No.3 (1989) pp. 257–263.
W. J. Martin, Mixed block designs, J. Combin. Designs, Vol. 6, No.2 (1998) pp. 151–163.
D. M. Mesner and P. Bhattacharya, Association schemes on triples and a ternary algebra, J. Combin. Theory Ser. A, Vol. 55, No.2 (1990) pp. 204–234.
D. M. Mesner and P. Bhattacharya, A ternary algebra arising from association schemes on triples, J. Algebra, Vol. 164, No.3 (1994) pp. 595–613.
A. Pott and M. Shrikhande, t-Designs with few intersection numbers, Discrete Math. Vol. 90, No.2 (1991) pp. 215–217.
J. D. H. Smith, Association schemes, superschemes, and relations invariant under permutation groups, Eur. J. Comb., Vol. 15, No.3 (1994) pp. 285–291.
V. T. Tonchev, Combinatorial configurations, Longman Scientific & Technical (1988).
J. Wojdylo, Relation algebras and t-vertex condition graphs, Eur. J. Comb., Vol. 19, No.8 (1998) pp. 981–986.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Martínez, L., Vera-López, A. Ring-Valued Assignments to the Points of a t-Design. Designs, Codes and Cryptography 25, 255–262 (2002). https://doi.org/10.1023/A:1014983312825
Issue Date:
DOI: https://doi.org/10.1023/A:1014983312825