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

2020/06/11 by Zenghui Fang, Fang, Zenghui, Junling Zhou +3
Computer Science · Engineering · #Cellular Automata and Applications #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2006.06921

openalex publication_date 2020/06/11 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate combinatorial constructions for w-cyclic\nholely group divisible packings with block size three (briefly by 3-HGDPs).\nFor any positive integers u,v,w with u\≡0,1~( bmod~3), the exact number\nof base blocks of a maximum w-cyclic 3-HGDP of type (u,w^v) is\ndetermined. This result is used to determine the exact number of codewords in a\nmaximum three-dimensional (u\× v\× w,3,1) optical orthogonal code\nwith at most one optical pulse per spatial plane and per wavelength plane.\n

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