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Designs, Codes and Cryptography

Erschienen in:

01.09.2015

Completely reducible super-simple designs with block size five and index two

verfasst von: Hengjia Wei, Hui Zhang, Gennian Ge

Erschienen in: Designs, Codes and Cryptography | Ausgabe 3/2015

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Abstract

Complete reducible super-simple (CRSS) designs are closely related to \(q\)-ary constant weight codes. A \((v,k,\lambda )\)-CRSS design is just an optimal \((v,2(k-1),k)_{\lambda +1}\) code. In this paper, we mainly investigate the existence of a \((v,5,2)\)-CRSS design and show that such a design exists if and only if \(v\equiv 1,5\pmod {20}\) and \(v\ge 21\), except possibly when \(v = 25\). Using this result, we determine the maximum size of an \((n,8,5)_3\) code for all \(n\equiv 0,1,4,5 \pmod {20}\) with the only length \(n=25\) unsettled. In addition, we also construct super-simple \((v,5,3)\)-BIBDs for \(v=45,65\).

Vorheriger Artikel Enhanced Boolean functions suitable for the filter model of pseudo-random generator

Nächster Artikel Practical-time attacks against reduced variants of MISTY1

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Titel: Completely reducible super-simple designs with block size five and index two
verfasst von: Hengjia Wei
Hui Zhang
Gennian Ge
Publikationsdatum: 01.09.2015
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 3/2015
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-014-9979-8

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