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On the existence of cyclic Steiner Quadruple systems SQS (2p)

✍ Scribed by Helmut Siemon

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
579 KB
Volume
97
Category
Article
ISSN
0012-365X

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✦ Synopsis

Siemon, H., On the existence of cyclic Steiner Quadruple Systems SQS(2p), Discrete Mathematics 97 (1991) 377-385. Subsequent to Kohler's result in [l], Satz 8, we show that strictly cyclic SQS(2p), p prime number and p = 53, 77 ( 120) exist if a certain number theoretic claim can be proved. We verified this claim for all admissible prime numbers p < S@lOOO.

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## Abstract Assmus [1] gave a description of the binary code spanned by the blocks of a Steiner triple or quadruple system according to the 2‐rank of the incidence matrix. Using this description, the author [13] found a formula for the total number of distinct Steiner triple systems on 2^__n__^βˆ’1 p