## Abstract The existence of a (__q,k__, 1) difference family in __GF__(__q__) has been completely solved for __k__โ=โ3,4,5,6. For __k__โ=โ7 only partial results have been given. In this article, we continue the investigation and use Weil's theorem on character sums to show that the necessary condi
The existence of (v, 4, 1) disjoint difference families withva prime power
โ Scribed by Dian-hua Wu; Jian-xiao Yang; Bi-chang Huang
- Publisher
- Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2008
- Tongue
- English
- Weight
- 184 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0168-9673
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The existence of a (q, k, 1) difference family in GF(q) has been completely solved for k = 3. For k = 4, 5 partial results have been given by Bose, Wilson, and Buratti. In this article, we continue the investigation and show that the necessary condition for the existence of a (q, k, 1) difference fa
For a prime power q = 1 (mod k(k-1)) does there exist a (q, k, 11 difference family in GF(q)? The answer to this question is affirmative for k=3 and also for k>3 provided that q is sufficiently large (Wilson's asymptotic existence theoremt but very little is known for k > 3 and q not large enough.
The existence of NRB [v, k] where k โฅ 7 and k + 1 is an even prime power is considered. We will show that there exists an NRB[kn+1, k] for all n > (3k where k + 1 is an even prime power, k โฅ 7 and b = k 3 k 4k 2 . The tools used to construct this bound include the frames extracted from a construct