Combinatorial constructions for optimal 2-D optical orthogonal codes with AM-OPPTS property |
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Authors: | Peipei Dai Jianmin Wang Jianxing Yin |
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Affiliation: | 1. Department of Mathematics, Soochow University, Suzhou, 215006, China
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Abstract: | 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. |
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