Constructions of 1 1/2-designs from symplectic geometry over finite fields

Chai, Zhao; Feng, Rong Quan; Zeng, Li

doi:10.1007/s10114-015-4716-4

Cited by 6 publications

(2 citation statements)

References 9 publications

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“…There are 45 negative intriguing sets of size 12 fixed by a group of order 1152, any two of them have 3 or 6 points in common. The corresponding SRG has parameters (45,32,22,24) that is the complement of the point graph of H(3, 4). (2) In NU (3,25), there is a negative intriguing set I of size 105, fixed by the group A 7 .…”

Section: The Paley Graph Srg(9 4 1 2)mentioning

confidence: 99%

Intriguing sets of strongly regular graphs and their related structures

Crnković,

Pavese,

Švob

2023

CDM

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Section: The Paley Graph Srg(9 4 1 2)mentioning

confidence: 99%

Intriguing sets of strongly regular graphs and their related structures

Crnković,

Pavese,

Švob

2023

CDM

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“…In [18], Olmez investigated the link between partial geometric designs and three‐weight codes, and in [13] Nowak and Olmez described a method that can often be used to determine the existence or nonexistence of a partial geometric design having specified automorphisms. Many researchers constructed partial geometric designs with various objects [7–9,11,14]. In this paper, we focus on partial geometric designs with block sizes three and four.…”

Section: Introductionmentioning

confidence: 99%

Partial geometric designs with block sizes three and four

Lei

Shan

2021

J of Combinatorial Designs

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In this paper, we focus on partial geometric designs with block sizes three and four. First, we show that a partial geometric design with block size three is a 2‐design, or a transversal design, or each line of a generalized quadrangle that is repeated λ times. Second, we introduce the concept of type of partial geometric designs with block size four and characterize partial geometric designs of type [λ,1,1] for some integer λ≥1.

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New partial geometric difference sets and partial geometric difference families

Michel

2016

Acta. Math. Sin.-English Ser.

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Olmez, in "Symmetric 1 1 2 -Designs and 1 1 2 -Difference Sets" (2014), introduced the concept of a partial geometric difference set (also referred to as a 1 1 2 -design), and showed that partial geometric difference sets give partial geometric designs. Nowak et al., in "Partial Geometric Difference Families" (2014), introduced the concept of a partial difference family, and showed that these also give partial geometric designs. It was shown by Brouwer et al. in "Directed strongly regular graphs from 1 1 2 -designs" (2012) that directed strongly regular graphs can be obtained from partial geometric designs. In this correspondence we construct several families of partial geometric difference sets and partial difference families with new parameters, thereby giving directed strongly regular graphs with new parameters. We also discuss some of the links between partially balanced designs, 2-adesigns (which were recently coined by Cunsheng Ding in "Codes from Difference Sets" (2015)), and partial geometric designs, and make an investigation into when a 2-adesign is partial geometric.

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Constructions of 1 1/2-designs from symplectic geometry over finite fields

Cited by 6 publications

References 9 publications

Intriguing sets of strongly regular graphs and their related structures

Intriguing sets of strongly regular graphs and their related structures

Partial geometric designs with block sizes three and four

New partial geometric difference sets and partial geometric difference families

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