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Maximum w ‐cyclic holey group divisible packings with block size three and applications to optical orthogonal codes
Author(s) -
Fang Zenghui,
Zhou Junling,
Wang Lidong
Publication year - 2021
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21797
Subject(s) - mathematics , combinatorics , block (permutation group theory) , plane (geometry) , block size , group (periodic table) , geometry , physics , computer science , computer security , quantum mechanics , key (lock)
In this paper we investigate combinatorial constructions for w ‐cyclic holey group divisible packings with block size three (3‐HGDPs). For any positive integers u , v , w with u ≡ 0 , 1 ( mod 3 ) , the exact number of base blocks of a maximum w ‐cyclic 3‐HGDP of type ( u , w v ) is determined. This result is used to determine the exact number of codewords in a maximum three‐dimensional ( u × v × w , 3 , 1 ) optical orthogonal code with at most one optical pulse per spatial plane and per wavelength plane.