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تسجيل مستخدم جديدMaximum $w$-cyclic holely group divisible packings with block size three and applications to optical orthogonal codes
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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 $uequiv0,1~(bmod~3)$, 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 $(utimes vtimes w,3,1)$ optical orthogonal code with at most one optical pulse per spatial plane and per wavelength plane.
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