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Designs, Codes and Cryptography

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01.08.2016

A construction and decomposition of orthogonal arrays with non-prime-power numbers of symbols on the complement of a Baer subplane

verfasst von: Kohei Yamada, Nobuko Miyamoto

Erschienen in: Designs, Codes and Cryptography | Ausgabe 2/2016

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Abstract

Fuji-Hara and Kamimura (Util Math 43:65–70, 1993) outlined a method for constructing orthogonal arrays of strength 2 on the complement of a Baer subplane, with \(q(q-1)\) symbols for a prime power \(q\). In this paper, we demonstrate that these orthogonal arrays can be decomposed into other orthogonal arrays of strength 2, with the same numbers of constraints and symbols but with smaller sizes and indices. In our construction, each orthogonal array of the decomposition can be obtained as an orbit of the point-set of a Baer subplane, under the action of a certain projective linear group. Furthermore, for \(q \equiv 2 \pmod 3\) and \(q > 2\), a series of the new orthogonal arrays cannot be obtained by Bush’s direct product construction, which is a classical method for constructing orthogonal arrays with non-prime-power numbers of symbols.

Vorheriger Artikel On Jacobi sums, difference sets and partial difference sets in Galois domains

Nächster Artikel Complete weight enumerators of some cyclic codes

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Titel: A construction and decomposition of orthogonal arrays with non-prime-power numbers of symbols on the complement of a Baer subplane
verfasst von: Kohei Yamada
Nobuko Miyamoto
Publikationsdatum: 01.08.2016
Verlag: Springer US
Erschienen in: Designs, Codes and Cryptography / Ausgabe 2/2016
Print ISSN: 0925-1022
Elektronische ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-015-0086-2

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