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Existence of (q, k, 1) difference families with q a prime power and k = 4, 5

✍ Scribed by K. Chen; L. Zhu

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
188 KB
Volume
7
Category
Article
ISSN
1063-8539

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✦ Synopsis

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 family in GF(q), i.e., q ≡ 1 (mod k(k -1)) is also sufficient for k = 4, 5. For general k, Wilson's bound shows that a (q, k, 1) difference family in GF(q) exists whenever q ≡ 1 (mod k(k -1)) and q > [k(k -1)/2] k(k-1) . An improved bound on q is also presented.

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