An extending theorem for s-resolvable t-designs

An extending theorem for s -resolvable t -designs is presented, which may be viewed as an extension of Qiu-rong Wu’s result. The theorem yields recursive constructions for s -resolvable t -designs, and mutually disjoint t -designs. For example, it can be shown that if there exists a large set LS [29...

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Bibliographic Details
Published in:Designs, codes, and cryptography codes, and cryptography, 2021-03, Vol.89 (3), p.589-597
Main Author: van Trung, Tran
Format: Article
Language:English
Subjects:
Coding and Information Theory
Computer Science
Cryptology
Discrete Mathematics in Computer Science
Theorems
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Summary:An extending theorem for s -resolvable t -designs is presented, which may be viewed as an extension of Qiu-rong Wu’s result. The theorem yields recursive constructions for s -resolvable t -designs, and mutually disjoint t -designs. For example, it can be shown that if there exists a large set LS [29](4, 5, 33), then there exists a family of 3-resolvable 4- ( 5 + 29 m , 6 , 5 2 m ( 1 + 29 m ) ) designs for m ≥ 1 , with 5 resolution classes. Moreover, for any given integer h ≥ 1 , there exist ( 5 · 2 h - 5 ) mutually disjoint simple 3- ( 3 + m ( 5 · 2 h - 3 ) , 4 , m ) designs for all m ≥ 1 . In addition, we give a brief account of t -designs derived from the result of Wu.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-020-00835-7