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Designs, Codes and Cryptography

, Volume 63, Issue 3, pp 305–319 | Cite as

Semicyclic 4-GDDs and related two-dimensional optical orthogonal codes

  • Kun Wang
  • Jianmin Wang
Article

Abstract

The existence problem for a semicyclic group divisible design (SCGDD) of type m n with block size 4 and index unity, denoted by 4-SCGDD, has been studied for any odd integer m to construct a kind of two-dimensional optical orthogonal codes (2-D OOCs) with the AM-OPPW (at most one-pulse per wavelength) restriction. In this paper, the existence of a 4-SCGDD of type m n is determined for any even integer m, with some possible exceptions. A complete asymptotic existence result for k-SCGDDs of type m n is also obtained for all larger k and odd integer m. All these SCGDDs are used to derive new 2-D OOCs with the AM-OPPW restriction, which are optimal in the sense of their sizes.

Keywords

Group divisible design Semicyclic Optical orthogonal code Two-dimensional Generalized Bhaskar Rao design 

Mathematics Subject Classification (2000)

05B40 94B65 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsSoochow UniversitySuzhouChina

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