Candelabra systems and designs

Mohácsy, Hedvig; Ray-Chaudhuri, D. K.

doi:10.1016/s0378-3758(02)00226-4

Cited by 69 publications

(69 citation statements)

References 10 publications

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“…There are many known Steiner 2 − designs but constructing Steiner > 2 it has proved to be much harder. In the case of = 3, Kageyama [11] has shown thatthere is 3 − ( , 4,1) design if andonly if the necessary arithmetic conditions are satisfied. But for larger k, even = 5, the result is far from complete.…”

Section: Literature Reviewmentioning

confidence: 99%

Construction of Some Resolvable <i>t</i>-designs

David¹

2017

SJAMS

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Abstract:The A t-design is a generation of balanced incomplete block design (BIBD) where λ is not restricted to the blocks in which a pair of treatments occurs but to the number of blocks in which any t treatments (t = 2,3…) occurs. The problem of finding all parameters (t, v, k, λ t ) for which t-(v, k, λ t ) design exists is a long standing unsolved problem especially with λ=1 (Steiner System) as no Steiner t-designs are known for t ≥ 6 when v > k. In this study t-design is constructed by relating known BIB designs, combinatorial designs and algebraic structures with t-designs. Additionally, an alternative approach for the construction of t-designs that provides a unified framework is also presented.

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Section: Literature Reviewmentioning

confidence: 99%

Construction of Some Resolvable <i>t</i>-designs

David¹

2017

SJAMS

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“…There are many known Steiner 2 − designs but constructing Steiner > 2 it has proved to be much harder. Wilson (1972aWilson ( ,1972b building upon the work of many including ( [3], [7], [10], and [11]) proved for = 2 , fixed k and sufficiently large v satisfying arithmetic conditions 2 −designs exist. There is no similar existence result yet for > 2.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Algebraic construction requires that a certain fixed (big) group to act as a group of automorphisms for the desired design. This technique was first formulated on paper by [11].…”

Section: Literature Reviewmentioning

confidence: 99%

Construction Procedure for Non-trivial T-designs

Chibayi¹

2017

AJTAS

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Abstract:A t-design is a generation of balanced incomplete block design (BIBD) where λ is not restricted to the blocks in which a pair of treatments occurs but to the number of blocks in which any treatments (t = 2,3…) occurs. The problem of finding all parameters (t, v, k, λ t ) for which t-(v, k, λ t ) design exists is a long standing unsolved problem especially with λ=1 (Steiner System) as no Steiner t-designs are known for t ≥ 6 when v > k. The objective of this study therefore to develop new methods of constructing t-designs with t ≥ 3 and λ ≥1. In this study t-design is constructed by relating known BIB designs, combinatorial designs and algebraic structures with t-designs.

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“…The first recursive construction for 3-GDDs is a special case of the fundamental construction for t-GDDs in [16 Proof. From the given HF (m, 6, 4, 3), we also have an HF (m, 6, 4, 3), (X, G, B, F), containing exactly one hole of size h and (m − h)/2 holes of size 2, which are mutually disjoint.…”

Section: Say That a T-gdd (X G B ) Is A Subdesign Of A T-gdd (X mentioning

confidence: 99%

A class of group divisible 3‐designs and their applications

Wang¹,

Ji²

2008

J of Combinatorial Designs

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Abstract:In this article, we first show that a group divisible 3-design with block sizes from {4, 6}, index unity and group-type 2 m exists for every integer m ≥ 4 with the exception of m = 5. Such group divisible 3-designs play an important role in our subsequent complete solution to the existence problem for directed H-designs DH λ (m, r, 4, 3)s. We also consider a way to construct optimal codes capable of correcting one deletion or insertion using the directed H-designs. In this way, the optimal single-deletion/insertion-correcting codes of length 4 can be constructed for all even alphabet sizes.

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Candelabra systems and designs

Cited by 69 publications

References 10 publications

Construction of Some Resolvable <i>t</i>-designs

Construction of Some Resolvable <i>t</i>-designs

Construction Procedure for Non-trivial T-designs

A class of group divisible 3‐designs and their applications

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Candelabra systems and designs

Cited by 69 publications

References 10 publications

Construction of Some Resolvable &lt;i&gt;t&lt;/i&gt;-designs

Construction of Some Resolvable &lt;i&gt;t&lt;/i&gt;-designs

Construction Procedure for Non-trivial T-designs

A class of group divisible 3‐designs and their applications

Contact Info

Product

Resources

About

Construction of Some Resolvable <i>t</i>-designs

Construction of Some Resolvable <i>t</i>-designs