Some combinatorial constructions for optical orthogonal codes

Yin, Jianxing

doi:10.1016/s0012-365x(97)00172-6

Cited by 164 publications

(147 citation statements)

References 25 publications

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“…When u = 14, by Lemma B.2 in Supporting Information, there exists a 2-cyclic 3-IGDD of type 2 (14,2) , which is also a 3-SCGDP of type 2 14 with J * (14 × 1 × 2, 3, 1) base blocks. When u = 26, by Lemma B.5 in Supporting Information, there exists a 2-cyclic 3-IGDD of type 2 (26,11) . Fill in the hole with a 3-SCGDP of type 2 11 with J * (11 × 1 × 2, 3, 1) base blocks from Corollary 2.6 to obtain a 3-SCGDP of type 2 26 with J * (26 × 1 × 2, 3, 1) base blocks.…”

Section: The Case Of U ≡ 2 (Mod 6)mentioning

confidence: 99%

“…When u = 26, by Lemma B.5 in Supporting Information, there exists a 2-cyclic 3-IGDD of type 2 (26,11) . Take a 3-SCGDP * of type 2 (11,5) with 32 base blocks from Example 5.1.…”

Section: The Case Of U ≡ 2 (Mod 6)mentioning

confidence: 99%

“…1-D OOCs were first suggested by [7] in 1989. Since then there are many researches on 1-D OOCs (see, e.g., [2,3,5,12,14,18,19,26]). 1-D OOCs spread optical pulses only in time domain.…”

Section: Introductionmentioning

confidence: 99%

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Determination of Sizes of Optimal Three‐Dimensional Optical Orthogonal Codes of Weight Three with the AM‐OPP Restriction

Wang

Chang

2016

J of Combinatorial Designs

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In this paper, we further investigate the constructions on three-dimensional (u × v × w, k, 1) optical orthogonal codes with the at most one optical pulse per wavelength/time plane restriction (briefly AM-OPP 3-D (u × v × w, k, 1)-OOCs) by way of the corresponding designs. Several new auxiliary designs such as incomplete holey group divisible designs and incomplete group divisible packings are introduced and therefore new constructions are presented. As a consequence, the exact number of codewords of an optimal AM-OPP 3-D (u × v × w, 3, 1)-OOC is finally determined for any positive integers v, w and u ≥ 3.

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Section: The Case Of U ≡ 2 (Mod 6)mentioning

confidence: 99%

“…When u = 26, by Lemma B.5 in Supporting Information, there exists a 2-cyclic 3-IGDD of type 2 (26,11) . Take a 3-SCGDP * of type 2 (11,5) with 32 base blocks from Example 5.1.…”

Section: The Case Of U ≡ 2 (Mod 6)mentioning

confidence: 99%

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Determination of Sizes of Optimal Three‐Dimensional Optical Orthogonal Codes of Weight Three with the AM‐OPP Restriction

Wang

Chang

2016

J of Combinatorial Designs

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“…When t ¼ bðv À 1Þ=kðk À 1Þc, the CPðk; 1; vÞ is called optimal. The following results are presented in [23]. It has been showed in [9] that an optimal ðv; 3; 1Þ-OOC exists if and only if v 6 ¼ 6t þ 2 with t 2 or 3 (mod 4).…”

Section: Introductionmentioning

confidence: 99%

“…In [23], the notation CPðk; 1; vÞ denotes a cyclic packing with order v, block size k, and index ¼ 1; each of its block orbits containing v blocks. A convenient way of viewing such a packing is from a difference family perspective.…”

Section: Introductionmentioning

confidence: 99%