Imprimitive cometric association schemes: Constructions and analysis

Journal of Algebraic Combinatorics

Volumn 25, Issue 4, 2007, Pages 399-415

  Martin, William J ^a,b   Muzychuk, Mikhail ^c   Williford, Jason ^a  

^a Worcester Polytechnic Institute   (United States)

^b Worcester Polytechnic Institute   (United States)

^c NETANYA ACADEMIC COLLEGE   (Israel)

Author keywords

Association scheme; Cometric; Imprimitive; Linked system of symmetric designs; Q polynomial; Spherical design

Indexed keywords

COMPUTATION THEORY; METRIC SYSTEM; POLYNOMIALS; PROBLEM SOLVING;

ASSOCIATION SCHEME; COMETRIC; LINKED SYSTEM OF SYMMETRIC DESIGNS; Q-POLYNOMIAL; SPHERICAL DESIGN;

GRAPH THEORY;

EID: 34247355423     PISSN: 09259899     EISSN: 15729192     Source Type: Journal    
DOI: 10.1007/s10801-006-0043-2     Document Type: Article

References (18)

1. E. Bannai and T. Ito, Algebraic Combinatorics I: Association Schemes, Benjamin-Cummings, Menlo Park, 1984.
2. A.E. Brouwer, A.M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer-Verlag, Berlin, 1989.
3. A.E. Brouwer, C.D. Godsil, J.H. Koolen, and W. J. Martin, "Width and dual width of subsets in metric and cometric association schemes," J. Combin. Th. Ser. A 102 (2003), 255-271.
4. D. de Caen and E.R. van Dam, "Association schemes related to Kasami codes and Kerdock sets," Des. Codes Cryptogr. 18 (1999), 89-102.
5. P.J. Cameron, "On groups with several doubly-transitive permutation representations," Math. Z. 128 (1972), 1-14.
6. P.J. Cameron and J.J. Seidel, "Quadratic forms over GF(2)," Proc. Koninkl. Nederl. Akademie van Wetenschappen, Series A, Vol. 76 Indag. Math. 35 (1973), 1-8.
7. D. Cerzo and H. Suzuki, "On imprimitive Q-polynomial schemes of exceptional type," Preprint, 2006.
8. E. van Dam, "Three-class association schemes," J. Alg. Combin. 10(1) (1999), 69-107.
9. P. Delsaite, "An algebraic approach to the association schemes of coding theory," Philips Res. Repts. Suppl. 10 (1973).
10. P. Delsarte, J.-M. Goethals, and J.J. Seidel, "Spherical codes and designs," Geom. Ded. 6 (1977), 363-388.
11. G.A. Dickie, "Q-polynomial structures for association schemes and distance-regular graphs," Ph.D. Thesis, University of Wisconsin-Madison, 1995.
12. A.D. Gardiner, "Antipodal covering graphs," J. Combin. Th. Ser. B 16 (1974), 255-273.
13. C.D. Godsil, Algebraic Combinatorics, Chapman and Hall, New York, 1993.
14. R. Mathon, "The systems of linked 2-(16,6,2) designs," Ars Comb. 11 (1981), 131-148.
15. A. Munemasa, "Spherical designs," in Handbook of Combinatorial Designs (2nd ed.), C.J. Colbourn and J.H. Dinitz (eds.), CRC Press, Boca Raton, 2006, Section VI.54, pp. 637-643.
16. R. Noda, "On homogeneous systems of linked symmetric designs," Math. Z. 138 (1974), 15-20.
17. H. Suzuki, "Imprimitive Q-polynomial association schemes," J. Alg. Combin. 7(2) (1998), 165-180.
18. P. Terwilliger, "The subconstituent algebra of an association scheme I," J. Alg. Combin. 1(4) (1992), 363-388.