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.
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Communicated by J. D. Key.
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Wang, K., Wang, J. Semicyclic 4-GDDs and related two-dimensional optical orthogonal codes. Des. Codes Cryptogr. 63, 305–319 (2012). https://doi.org/10.1007/s10623-011-9556-3
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DOI: https://doi.org/10.1007/s10623-011-9556-3
Keywords
- Group divisible design
- Semicyclic
- Optical orthogonal code
- Two-dimensional
- Generalized Bhaskar Rao design