Maximum w-cyclic holely group divisible packings with block size three and applications to optical orthogonal codes

06/12/2020

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by   Zenghui Fang, et al.

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In this paper we investigate combinatorial constructions for w-cyclic holely group divisible packings with block size three (briefly by 3-HGDPs). For any positive integers u,v,w with u≡0,1 ( 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.