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

01-04-2015

Optimal three-dimensional optical orthogonal codes of weight three

Author: Kenneth W. Shum

Published in: Designs, Codes and Cryptography | Issue 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.
previous article Demi-matroids from codes over finite Frobenius rings
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Metadata
Title
Optimal three-dimensional optical orthogonal codes of weight three
Author
Kenneth W. Shum
Publication date
01-04-2015
Publisher
Springer US
Published in
Designs, Codes and Cryptography / Issue 1/2015
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-013-9894-4

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