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On simple radical difference families

✍ Scribed by Marco Buratti

Book ID
102310862
Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
345 KB
Volume
3
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

For q a prime power and k odd (even), we define a (q,k,1) difference family to be radical if each base block is a coset of the __k__th roots of unity in the multiplicative group of GF(q) (the union of a coset of the (k βˆ’ 1)th roots of unity in the multiplicative group of GF(q) with zero). Such a family will be denoted by RDF. The main result on this subject is a theorem dated 1972 by R.M. Wilson; it is a sufficient condition for the existence of a (q,k, 1)‐RDF for any k. We improve this result by replacing Wilson's condition with another sufficient but weaker condition, which is proved to be necessary at least for k β©½ 7. As a consequence, we get new difference families and hence new Steiner 2‐designs. Β© 1995 John Wiley & Sons, Inc.

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✍ Marco Buratti πŸ“‚ Article πŸ“… 1995 πŸ› John Wiley and Sons 🌐 English βš– 485 KB

In [2] R. C. Bose gives a sufficient condition for the existence of a (q, 5, 1) difference family in (GF(q), +)-where q = 1 mod 20 is a prime power-with the property that every base block is a coset of the 5th roots of unity. Similarly he gives a sufficient condition for the existence of a (q,4,1) d