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On resolvable Steiner 2-designs and maximal arcs in projective planes [article]

Vladimir D. Tonchev
2016 arXiv   pre-print
A combinatorial characterization of resolvable Steiner 2-(v,k,1) designs embeddable as maximal arcs in a projective plane of order (v-k)/(k-1) is proved, and a generalization of a conjecture by Andries  ...  Acknowledgments The author wish to thank the anonymous referees for carefully reading the manuscript and suggesting several improvements, including the open question formulated in Remark 2.2.  ...  A 2-(2 2t−1 − 2 t−1 , 2 t−1 , 1) design arising from a maximal (2 2t−1 − 2 t−1 ; 2 t−1 )-arc A is called an oval design [2, 8.4] , in reference to the fact that the corresponding maximal (2 t +2; 2)-arc  ... 
arXiv:1606.00697v1 fatcat:cw4mxinjxfdszfa5z6v7qzqhxi

Maximal (120,8)-arcs in projective planes of order 16 and related designs [article]

Vladimir D. Tonchev, Tim Wagner
2017 arXiv   pre-print
The resolutions and maximal sets of compatible resolutions of all 2-(120,8,1) designs arising frommaximal (120,8)-arcs in the known projective planes of order 16 are computed.  ...  It is shown that each of these designs is embeddable in a unique way in a projective plane of order 16.  ...  Royle for graciously providing the files with the data concerning the hyperovals in the known projective planes of order 16, and Tim Penttila for the helpful discussion and for bringing to our attention  ... 
arXiv:1702.06909v1 fatcat:47vomqtxxbhhlovt5idgzyqx44

On resolvable Steiner 2-designs and maximal arcs in projective planes

Vladimir D. Tonchev
2016 Designs, Codes and Cryptography  
A combinatorial characterization of resolvable Steiner 2-(v, k, 1) designs embeddable as maximal arcs in a projective plane of order (v − k)/(k − 1) is proved, and a generalization of a conjecture by Andries  ...  Acknowledgments The author wish to thank the anonymous referees for carefully reading the manuscript and suggesting several improvements, including the open question formulated in Remark 2.2.  ...  A 2-(2 2t−1 − 2 t−1 , 2 t−1 , 1) design arising from a maximal (2 2t−1 − 2 t−1 ; 2 t−1 )-arc A is called an oval design [2, 8.4] , in reference to the fact that the corresponding maximal (2 t +2; 2)-arc  ... 
doi:10.1007/s10623-016-0243-2 fatcat:adiyvbu3urg3pprp3thb656ycy

Maximal arcs and related designs

Tran van Trung
1991 Journal of combinatorial theory. Series A  
It turns out that the existence of a maximal arc in a 2-design implies the existence of another 2-design. Therefore it would be worth investigating maximal arcs in 2-designs.  ...  Then a residual design has parameters 2 -(v-k, v -1, k, k -/1, 2). LEMMA 1.6. A maximal n-arc in a residual design is a maximal n-arc in the corresponding symmetric design.  ... 
doi:10.1016/0097-3165(91)90052-i fatcat:dmflilcibvbudgf2immqoesa4i

Maximal Arcs, Codes, and New Links Between Projective Planes of Order 16

Mustafa Gezek, Rudi Mathon, Vladimir D. Tonchev
2020 Electronic Journal of Combinatorics  
In this paper we consider binary linear codes spanned by incidence matrices of Steiner 2-designs associated with maximal arcs in projective planes of even order, and their dual codes.  ...  A conjecture concerning the codes of maximal arcs in $PG(2,2^m)$ is formulated.  ...  D ⊥ ) as a design embeddable in P (resp. P ⊥ ) as a maximal arc. Two maximal arcs A , A in a projective plane P are equivalent if there is a collineation of P that maps A to A .  ... 
doi:10.37236/9008 fatcat:ejwt2gdt6fbjxjh53tdnjrx57u

Maximal arcs, codes, and new links between projective planes [article]

Mustafa Gezek, Rudi Mathon, Vladimir D. Tonchev
2020 arXiv   pre-print
In this paper we consider binary linear codes spanned by incidence matrices of Steiner 2-designs associated with maximal arcs in projective planes of even order, and their dual codes.  ...  A conjecture concerning the codes of maximal arcs in PG(2,2^m) is formulated.  ...  D ⊥ ) as a design embeddable in P (resp. P ⊥ ) as a maximal arc. Two maximal arcs A ′ , A ′′ in a projective plane P are equivalent if there is a collineation of P that maps A ′ to A ′′ .  ... 
arXiv:2001.11431v2 fatcat:vxaubkplbzg6dlzepn72ksftgy

Maximal arcs and group divisible designs

Alan Rahilly
1990 Bulletin of the Australian Mathematical Society  
design of the dual maximal arc of V\ is a (?  ...  In this paper we use maximal arcs of a certain type in symmetric designs to construct two infinite families of semiregular, group divisible designs whose duals are also group divisible.  ... 
doi:10.1017/s0004972700018037 fatcat:7nqnj7oo5re3zo62vwflviblma

Designs constructed from maximal arcs

D.R. Stinson
1991 Discrete Mathematics  
In this paper, we give constructions for various types of designs using maximal arcs in projective planes.  ...  In memory of Egmont Kiihler. Abstract Stinson, D.R., Designs constructed from maximal arcs, Discrete Mathematics 97 (1991) 387-393.  ...  Added in proof In [20] , De Clerck presents some results similar to those proved here. In particular, he gives a construction similar to Theorem 3.3.  ... 
doi:10.1016/0012-365x(91)90453-9 fatcat:625yo45hxfd43ioku6gnkevofq

Construction of block designs and related results

Elizabeth Jane Morgan
1978 Bulletin of the Australian Mathematical Society  
In Chapter 2 the concept of a maximal arc in a finite projective plane is generalised to the case of an arbitrary balanced incomplete block design, and the "internal structure" of designs possessing maximal  ...  Families of partially balanced designs are produced in some instances from designs with maximal arcs. The remaining three chapters contain different construction methods for balanced designs.  ...  In Chapter 2 the concept of a maximal arc in a finite projective plane is generalised to the case of an arbitrary balanced incomplete block design, and the "internal structure" of designs possessing maximal  ... 
doi:10.1017/s0004972700008546 fatcat:rbaekphbybctdanvu27zzr7yaa

Page 5348 of Mathematical Reviews Vol. , Issue 92j [page]

1992 Mathematical Reviews  
In particular if there is a maximal n-arc in a design, then there is a maximal n’- arc with n’ = (r—A)/n.  ...  Actually a maximal n-arc is just another 2-design embedded in a very particular way into the original one,  ... 

Maximal arcs in Steiner systems S(2,4,v)

Malcolm Greig, Alexander Rosa
2003 Discrete Mathematics  
A maximal arc in a Steiner system S(2; 4; v) is a set of elements which intersects every block in either two or zero elements.  ...  We describe methods of constructing an S(2; 4; v) with a maximal arc, and settle the longstanding su ciency question in a strong way.  ...  Also, in [13] , an S(2; 4; 40) with a maximal arc was constructed. In this article, we describe methods to construct S(2; 4; v)'s with a maximal arc.  ... 
doi:10.1016/s0012-365x(02)00609-x fatcat:2gg272xya5erfloillspjrq3w4

Page 43 of Journal of Systems Management Vol. 26, Issue 9 [page]

1975 Journal of Systems Management  
PARSONS Maximal Representing a system as a network of nodes and interconnecting arcs is a familiar device which can be very useful in the analysis of certain system design problems.  ...  The key is that the design objective can be translated into a network configuration objective which in turn can be developed through the use of an available network analysis technique.  ... 

Exact and Approximate Algorithms for Topological Design of Wide Area Networks with Non-simultaneous Single Commodity Flows [chapter]

Andrzej Kasprzak
2003 Lecture Notes in Computer Science  
The problem consists in selection of the nonsimultaneous single commodity flow routes, channel capacities and the wide area network topology in order to maximize the value of the min-max flow subject to  ...  The problem is concerned with designing of wide area computer networks.  ...  The value ( ) s X V is maximal iff the maximal flows between every pair of nodes in S s are equal to contains only arcs from the sets A and F r which are not changed in every successor of S r .  ... 
doi:10.1007/3-540-44864-0_82 fatcat:rt3lbd42knh4rbunj34l7jba2i

Factors Study Influencing on Numerical Simulation of Aircraft Windshield against Bird Strike

F.S. Wang, Z.F. Yue, W.Z. Yan
2011 Shock and Vibration  
The windshield structure is composed of windshield, framework, arc-frame and gasket.  ...  The results showed that these factors must be taken into account when FE analysis method is applied to aircraft anti-bird design.  ...  The designed figures of aircraft windshield, framework and arc-frame in UG software are shown in Figs 2 and 3, respectively. The FE models of windshield and windshield structure 3.1.  ... 
doi:10.1155/2011/304541 fatcat:vrocvimsdbgjniqgqbfd3xfjji

On symmetric and quasi-symmetric designs with the symmetric difference property and their codes

Dieter Jungnickel, Vladimir D Tonchev
1992 Journal of combinatorial theory. Series A  
A maximal 2"~ ' -arc in a symmetric design with parameters (1) contains 2"' points, and the blocks disjoint from such an arc form a maximal 2"-'-arc in the dual design. Proof.  ...  Moreover, the blocks disjoint from the arc form a maximal n'-arc in the dual design where n' = (v -p)/n.  ... 
doi:10.1016/0097-3165(92)90097-e fatcat:576ioeu4hbd6rok5werdydr3ka
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