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Designs, Codes and Cryptography

Erschienen in:

01.01.2015

Group divisible designs with block size four and group type \(g^um^1\)

verfasst von: Hengjia Wei, Gennian Ge

Erschienen in: Designs, Codes and Cryptography | Ausgabe 1/2015

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Abstract

Non-uniform group divisible designs have been studied by numerous researchers in the past two decades due to their vital applications in the constructions for other types of designs. Much progress has been made for the existence of \(\{4\}\)-GDDs of type \(g^um^1\), especially when \(gu\) is even. The corresponding problem for block size three had been solved by Colbourn et al. (J Comb Theory Ser A 59:73–89, 1992). In this paper, we consider the entire existence problem for such \(\{4\}\)-GDDs. We show that, for each given g, up to a small number of undetermined cases of \(u\), the necessary conditions on \((u,m)\) for the existence of a \(\{4\}\)-GDD of type \(g^um^1\) are also sufficient.

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Nächster Artikel Erratum to: Intersection of Hamming codes avoiding Hamming subcodes

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Titel: Group divisible designs with block size four and group type
verfasst von: Hengjia Wei
Gennian Ge
Publikationsdatum: 01.01.2015
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 1/2015
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-013-9854-z

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