Linearly Derived Steiner Triple Systems
نویسنده
چکیده
منابع مشابه
NS1D0 Sequences and Anti-Pasch Steiner Triple Systems
We present an algorithmic construction of anti-Pasch Steiner triple systems for orders congruent to 9 mod 12. This is a Bose-type method derived from a particular type of 3-triangulations generated from non-sum-one-diierence-zero sequences (NS1D0 sequences). We introduce NS1D0 sequences and describe their basic properties; in particular we develop an equivalence between the problem of nding NS1...
متن کاملAutomorphisms of Steiner triple systems
Abstract: Steiner triple systems are among the simplest and most intensively studied combinatorial designs. Their origins go back to the 1840s, and there exists by now a sizeable literature on the topic. In 1980, Babai proved that almost all Steiner triple systems have no nontrivial automorphism. On the other hand, there exist Steiner triple systems with large automorphism groups. We will discu...
متن کاملIsomorphisms of Infinite Steiner Triple Systems
An infinite countable Steiner triple system is called universal if any countable Steiner triple system can be embedded into it. The main result of this paper is the proof of non-existence of a universal Steiner triple system. The fact is proven by constructing a family S of size 2 of infinite countable Steiner triple systems so that no finite Steiner triple system can be embedded into any of th...
متن کاملHamilton Decompositions of Block-Intersection Graphs of Steiner Triple Systems
Block-intersection graphs of Steiner triple systems are considered. We prove that the block-intersection graphs of non-isomorphic Steiner triple systems are themselves non-isomorphic. We also prove that each Steiner triple system of order at most 15 has a Hamilton decomposable block-intersection graph.
متن کاملIdentical twin Steiner triple systems
Two Steiner triple systems, each containing precisely one Pasch configuration which, when traded, switches one system to the other, are called twin Steiner triple systems. If the two systems are isomorphic the systems are called identical twins. Hitherto, identical twins were only known for orders 21, 27 and 33. In this paper we construct infinite families of identical twin Steiner triple systems.
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عنوان ژورنال:
- Des. Codes Cryptography
دوره 13 شماره
صفحات -
تاریخ انتشار 1998