Combinatorial constructions for optimal 2-D optical orthogonal codes with AM-OPPTS property

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• 作者：Peipei Dai (1)
  Jianmin Wang (1)
  Jianxing Yin (1)
  
• 关键词：Two ; dimensional optical orthogonal code ; Upper bound ; Holey packing ; Automorphism group ; Mixed ; difference ; 05B40 ; 94B65
• 刊名：Designs, Codes and Cryptography
• 出版年：2014
• 出版时间：May 2014
• 年：2014
• 卷：71
• 期：2
• 页码：315-330
• 全文大小：246 KB
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• 作者单位：Peipei Dai (1)
  Jianmin Wang (1)
  Jianxing Yin (1)
  
  1. Department of Mathematics, Soochow University, Suzhou, 215006, China
  
• ISSN：1573-7586

文摘

We develop a new one-to-one correspondence between a two-dimensional (m?× n,?k,?ρ) optical orthogonal code (2-D (m?× n,?k,?ρ)-OOC) with AM-OPPTS (at most one-pulse per time slot) property and a certain combinatorial subject, called an n-cyclic holey packing of type m n . By this link, an upper bound on the size of a 2-D (m?× n,?k,?ρ)-OOC with AM-OPPTS property is derived. Afterwards, we employ combinatorial methods to construct infinitely many 2-D (m?× n,?k,?1)-OOCs with AM-OPPTS property, whose existence was previously unknown. All these constructions meet the upper bounds with equality and are thus optimal.