Directed Quadruple Designs

Soltankhah, Nasrin

doi:10.1007/978-1-4613-3554-2_20

Cited by 3 publications

(2 citation statements)

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“…The above necessary conditions for the existence of a DH λ (m, r, 4, 3) have been proved to be sufficient for r = 1 by Levenshtein [11], Soltankhah [19], Grannell, Griggs and Quinn [4]. Before handling the case where r > 1, we need to present two recursive constructions.…”

Section: Directed H-design Dhmentioning

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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Section: Directed H-design Dhmentioning

confidence: 99%

A class of group divisible 3‐designs and their applications

Wang¹,

Ji²

2008

J of Combinatorial Designs

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“…However, for t 3, only the spectrum of 3-(v, 4, 1)DD has been known. Soltankhah, in [7], gave the following necessary and sufficient condition of the existence of 3-(v, 4, 1)DD. The resolvable Steiner quadruple systems have been the focus of attention by many researchers, and there are a lot of results (see, for example, [2,3]).…”

Section: Introductionmentioning

confidence: 97%

Spectrum of resolvable directed quadruple systems

Wang

2010

Front. Math. China

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A t-(v, k, 1) directed design (or simply a t-(v, k, 1)DD) is a pair (S, T ), where S is a v-set and T is a collection of k-tuples (called blocks) of S, such that every t-tuple of S belongs to a unique block. The t-(v, k, 1)DD is called resolvable if T can be partitioned into some parallel classes, so that each parallel class is a partition of S. It is proved that a resolvable 3-(v, 4, 1)DD exists if and only if v ≡ 0 (mod 4).

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