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

01.04.2015

Optimal three-dimensional optical orthogonal codes of weight three

verfasst von: Kenneth W. Shum

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

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Abstract

Using polarization technique in optical code division multiple access, we can schedule the transmission of optical pulses in spatial domain, in addition to the frequency domain and time domain. An optical orthogonal code (OOC) which spreads in these dimensions is called a three-dimensional (3-D) OOC. In this paper, we study 3-D OOC with at most one optical pulse per wavelength/time plane, which have the favorable property that the Hamming auto-correlation is identically equal to 0. An upper bound on the number of codewords for general Hamming cross-correlation requirement is given. A 3-D OCC with at most one pulse per wavelength/time plane and Hamming cross-correlation no more than 1 is shown to be equivalent to a generalized Bhaskar Rao group divisible design (GBRGDD), signed over a cyclic group. Through this equivalence, necessary and sufficient conditions for the existence of GBRGDD of weighted 3, signed over a cyclic group, are derived.
Vorheriger Artikel Demi-matroids from codes over finite Frobenius rings
Nächster Artikel On relative constant-weight codes
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Metadaten
Titel
Optimal three-dimensional optical orthogonal codes of weight three
verfasst von
Kenneth W. Shum
Publikationsdatum
01.04.2015
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/s10623-013-9894-4

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