Existence of (q, 7, 1) difference families with q a prime power

Journal of Combinatorial Designs

Volumn 10, Issue 2, 2002, Pages 126-138

  Chen, K ^a   Wei, R ^b   Zhu, L ^c  

^a YANCHENG TEACHERS UNIVERSITY   (China)

^b LAKEHEAD UNIVERSITY   (Canada)

^c SOOCHOW UNIVERSITY   (China)

Author keywords

Block design; Character sum; Cyclotomic class; Difference family; Finite field

Indexed keywords

EID: 0345017655     PISSN: 10638539     EISSN: 15206610     Source Type: Journal    
DOI: 10.1002/jcd.998     Document Type: Article

References (22)

1. I. Anderson, S. D. Cohen, N. J. Finizio, An existence theorem for cyclic triplewhist tournaments, Discrete Math 138(1995), 31-41.
2. Th. Beth, D. Jungnickel, H. Lenz, Design theory, Bibliographisches Institut, Zurich, 1985.
3. R. C. Bose, On the construction of balanced incomplete block designs, Ann Eugenics 9(1939), 353-399.
4. M. Buratii, Existence of Z-cyclic triplewhist tournaments for a prime number of players, J Combin Theory (A) 90(2000), 315-325.
5. M. Buratti, Constructions for (q, k, 1) difference families with q a prime power and k = 4, 5, Discrete Math 138(1995), 169-175.
6. M. Buratti, Improving two theorems of Bose on difference families, J Combin Designs 3(1995), 15-24.
7. M. Buratti, On simple radical difference families, J Combin Designs 3(1995), 161-168.
8. C. J. Colbourn and J. H. Dinitz (Editors), CRC Handbook of Combinatorial Designs, CRC Press, New York, 1996.
9. K. Chen, G. H. J. Van Rees, L. Zhu, V (m, t) and its variants, J Stat Plan Infer 95(2001), 143-160.
10. K. Chen and L. Zhu, Existence of APAV (q, k) with q a prime power = 3 (mod 4) and k odd > 1, J Combin Designs 7(1999), 57-68.
11. K. Chen and L. Zhu, Existence of (q, k, 1) difference families with q a prime power and k = 4, 5, J Combin Designs 7(1999), 21-30.
12. K. Chen and L. Zhu, Existence of (q, 6, 1) difference families with q a prime power, Designs Codes Cryptogr 15(1998), 167-173. (Pubitemid 128508039)
13. K. Chen and L. Zhu, Improving Wilson's bound on difference families, Utilitas Math, 55(1999), 189-200.
14. K. Chen and L. Zhu, The spectrum Q (k, A) of coset difference arrays with k = 2\ + 1, JCMCC, to appear.
15. M. Greig, Some balanced incomplete block design constructions, Congr Numer 77(1990), 121-134.
16. K. B. Gross, On the maximal number of pairwise orthogonal Steiner triple systems, J Combin Theory Ser. A 19(1975), 256-263.
17. C. H. A. Ling, Y. Lu, G. H. J. Van Rees, L. Zhu, V (m, t) s for m = 4, 5, 6, J Stat Plan Infer 86(2000), 515-525.
18. R. Lidl and H. Niederreiter, Finite fields, In: Encyclopedia of Mathematics and Its Applications, Vol. 20. Cambridge University Press, Cambridge, 1983.
19. G. McNay, Cohen's sieve with quadratic conditions, Utilitas Math 49(1996), 191-201. (Pubitemid 126310464)
20. E. Netto, Zur theorie der tripelsysteme, Math Ann 42(1893), 143-152.
21. T. Szonyi, Some applications of algebraic curves in finite geometry and combinatorics, London Mathematical Society Lecture Notes, series 241, Cambridge University Press, 1997, pp. 197-236.
22. R. M. Wilson, Cyclotomy and difference families in elementary abelian groups, J Number Theory 4(1972), 17-47.