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On Cyclically Resolvable Cyclic Steiner 2-Designs

โœ Scribed by Clement Lam; Ying Miao

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
133 KB
Volume
85
Category
Article
ISSN
0097-3165

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โœฆ Synopsis

In this article, we present a direct construction for cyclically resolvable cyclic Steiner 2-designs which is applicable irrespective of the parity of the block size. As an example, by using Weil's theorem on character sums, this construction gives an infinite series of cyclically resolvable cyclic Steiner 2-designs with block size 4 on 4p points, where p=12t+1 is a prime greater than 22581507 and t is odd. With the aid of a computer and some ad hoc constructions, we show that such designs exist also for primes less than 22581507. By applying a known recursive method, we construct other cyclically resolvable cyclic Steiner 2-designs with block size 4 on 4q points, where q is a product of primes of the form 12t+1 and t is odd.

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