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

✍ Scribed by K. Chen; R. Wei; L. Zhu

Publisher: John Wiley and Sons
Year: 2002
Tongue: English
Weight: 134 KB
Volume: 10
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.998

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✦ Synopsis

Abstract

The existence of a (q,k, 1) difference family in GF(q) has been completely solved for k = 3,4,5,6. For k = 7 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 condition for the existence of a (q,7,1) difference family in GF(q), i.e. q ≡ 1; (mod 42) is also sufficient except for q = 43 and possibly except for q = 127, q = 211, q = 31^6^ and primes q∈ [261239791, 1.236597 × 10^13^] such that $(-3)^{q-1\over 14} = 1$ in GF(q). © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 126–138, 2002; DOI 10.1002/jcd.998

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