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Constructions of optimal optical orthogonal codes with weight five
Author(s) -
Ma Shikui,
Chang Yanxun
Publication year - 2005
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.20022
Subject(s) - mathematics , combinatorics , integer (computer science) , character (mathematics) , skew , product (mathematics) , discrete mathematics , computer science , telecommunications , geometry , programming language
Several direct constructions via skew starters and Weil's theorem on character sum estimates are given in this paper for optimal ( gv , 5, 1) optical orthogonal codes (OOCs) where 60 ≤ g ≤ 180 satisfying g ≡ 0 (mod 20) and v is a product of primes greater than 5. These improve the known existence results on optimal OOCs. Especially, we provide an optimal ( v , 5, 1)‐OOC for any integer v ≡ 60, 420, 660, 780, 1020, 1140, 1380, 1740 (mod 1800). © 2004 Wiley Periodicals, Inc. J Combin Designs 13: 54–69, 2005.