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

Dai, Peipei; Wang, Jianmin; Yin, Jianxing

doi:10.1007/s10623-012-9733-z

Cited by 7 publications

(16 citation statements)

References 27 publications

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“…Combining the 8-cyclic 3-IGDD of type (16,8) 8 from Lemma A.1 in Supporting Information, we have a 2 n -cyclic 3-IGDD of type (2 n+1 , 2 n ) 8 for all n ≥ 1. Inflate it by a 3-SCGDD of type w ′ 3 from Corollary 2.6, we obtain the required w-cyclic 3-IGDD of type (2w, w) 8 .…”

Section: Lemma 47mentioning

confidence: 92%

“…Inflate it by a 3-SCGDD of type w ′ 3 from Corollary 2.6, we obtain the required w-cyclic 3-IGDD of type (2w, w) 8 . ✷ Proof By Lemma 4.11, a 2-cyclic 3-IGDD of type (2v, 2) u exists.…”

Section: Lemma 47mentioning

confidence: 94%

“…Theorem 3.14 [8] A (1, g, t)-cyclic 3-HGDD of type (u, g t ) exists if and only if u, t ≥ 3, (t − 1)(u − 1)g ≡ 0 (mod 2) and t(t − 1)u(u − 1)g ≡ 0 (mod 6), except for u = t = 3 and g ≡ 0 (mod 2).…”

Section: Construction 38mentioning

confidence: 99%

“…Then there exists a (g, t, 1)-cyclic 3-HGDD of type (u, g t ) for any g ≡ t ≡ 3 (mod 6). Dai, et al [8] discussed the existence of a (1, g, t)-cyclic 3-HGDDs of type (u, g t ), which is called a g-cyclic 3-HGDDs of type (u, g t ). We quote the result as follows.…”

Section: Construction 38mentioning

confidence: 99%

“…When u ≥ 20, start with a 4-cyclic 3-GDD of type 24 (u−2)/6 from Corollary 2.6. Apply Construction 4.21 with a 4-cyclic 3-IGDD of type 4 (8,2) to obtain a 4-cyclic 3-IGDD of type 4 (u,2) . ✷ Lemma 4.28 There exists a 6-cyclic 3-IGDD of type 6 (u,6) for any u ≡ 2 (mod 12) and u ≥ 14.…”

Section: Construction 421 (Filling Construction-iv) Suppose That Thementioning

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: Lemma 47mentioning

confidence: 92%

“…Inflate it by a 3-SCGDD of type w ′ 3 from Corollary 2.6, we obtain the required w-cyclic 3-IGDD of type (2w, w) 8 . ✷ Proof By Lemma 4.11, a 2-cyclic 3-IGDD of type (2v, 2) u exists.…”

Section: Lemma 47mentioning

confidence: 94%

Section: Construction 38mentioning

confidence: 99%

Section: Construction 38mentioning

confidence: 99%

Section: Construction 421 (Filling Construction-iv) Suppose That Thementioning

confidence: 99%

See 3 more Smart Citations

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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Bounds and Constructions for Two‐Dimensional Variable‐Weight Optical Orthogonal Codes

Cheng

Jiang

2013

J of Combinatorial Designs

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Optical orthogonal codes (1D constant‐weight OOCs or 1D CWOOCs) were first introduced by Salehi as signature sequences to facilitate multiple access in optical fibre networks. In fiber optic communications, a principal drawback of 1D CWOOCs is that large bandwidth expansion is required if a big number of codewords is needed. To overcome this problem, a two‐dimensional (2D) (constant‐weight) coding was introduced. Many optimal 2D CWOOCs were obtained recently. A 2D CWOOC can only support a single QoS (quality of service) class. A 2D variable‐weight OOC (2D VWOOC) was introduced to meet multiple QoS requirements. A 2D VWOOC is a set of 0, 1 matrices with variable weight, good auto, and cross‐correlations. Little is known on the construction of optimal 2D VWOOCs. In this paper, new upper bound on the size of a 2D VWOOC is obtained, and several new infinite classes of optimal 2D VWOOCs are obtained.

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Constructions of Strictlym-Cyclic and Semi-Cyclic H(m,n,4,3)

Bao

Ji²

2015

J. Combin. Designs

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An H(m, n, 4, 3) is a triple (X, T , B), where X is a set of mn points, T is a partition of X into m disjoint sets of size n and B is a set of 4-element transverses of T , such that each 3-element transverse of T is contained in exactly one of them. If the full automorphism group of an H(m, n, 4, 3) admits an automorphism α consisting of n cycles of length m (resp. m cycles of length n), then this H(m, n, 4, 3) is called m-cyclic (resp. semi-cyclic). Further, if all blockorbits of an m-cyclic (resp. semi-cyclic) H(m, n, 4, 3) are full, then it is called strictly cyclic. In this paper, we construct some infinite classes of strictly m-cyclic and semi-cyclic H(m, n, 4, 3), and use them to give new infinite classes of perfect two-dimensional optical orthogonal codes with maximum collision parameter λ = 2 and AM-OPPTS/AM-OPPW property.

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

Cited by 7 publications

References 27 publications

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

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

Bounds and Constructions for Two‐Dimensional Variable‐Weight Optical Orthogonal Codes

Constructions of Strictlym-Cyclic and Semi-Cyclic H(m,n,4,3)

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