Semicyclic 4-GDDs and related two-dimensional optical orthogonal codes

Wang, Kun; Wang, Jianmin

doi:10.1007/s10623-011-9556-3

Cited by 15 publications

(4 citation statements)

References 27 publications

(42 reference statements)

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“…Some constructions of AM‐OPPW 2D

(m \times n, k, λ)

‐OOCs can be found in . Some constructions of AM‐OPPTS 2‐D

(m \times n, k, λ)

‐OOCs can be found in .…”

Section: M‐cyclic H(mn43)′s Applicationmentioning

confidence: 99%

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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“…Some constructions of AM‐OPPW 2D

(m \times n, k, λ)

‐OOCs can be found in . Some constructions of AM‐OPPTS 2‐D

(m \times n, k, λ)

‐OOCs can be found in .…”

Section: M‐cyclic H(mn43)′s Applicationmentioning

confidence: 99%

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

Bao

Ji²

2015

J. Combin. Designs

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“…There is a 3-SCGDD of type m n if and only if n ≥ 3 and Lemma 2.4 [31,32] There is a 4-SCGDD of type m n if and only if n ≥ 4, m(n−1) ≡ 0 (mod 3) and mn(n − 1) ≡ 0 (mod 12), except when n = 4 or (m, n) ∈ {(2, 10), (4, 7), (6, 5)}, and possibly when (1) n = 5, m ≡ ±6 (mod 36) and m ≥ 30, (2) n = 7, m ≡ ±4 (mod 24) and m ≥ 20, (3) n = 10, m ≡ ±2 (mod 12) and m ≥ 10.…”

Section: Lemma 23 [18]mentioning

confidence: 99%

Semi-cyclic holey group divisible designs with block size three

Feng

Wang

Chang

2013

Des. Codes Cryptogr.

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In this paper we discuss the existence problem for a semi-cyclic holey group divisible design of type (n, m t ) with block size 3, which is denoted by a 3-SCHGDD of type (n, m t ). When n = 3, a 3-SCHGDD of type (3, m t ) is equivalent to a (3, mt; m)-cyclic holey difference matrix, denoted by a (3, mt; m)-CHDM.It is shown that there is a (3, mt; m)-CHDM if and only if (t − 1)m ≡ 0 (mod 2) and t ≥ 3 with the exception of m ≡ 0 (mod 2) and t = 3. When n ≥ 4, the case of t odd is considered. It is established that if t ≡ 1 (mod 2) and n ≥ 4, then there exists a 3-SCHGDD of type (n, m t ) if and only if t ≥ 3 and (t − 1)n(n − 1)m ≡ 0 (mod 6) with some possible exceptions of n = 6 and 8. The main results in this paper have been used to construct optimal two-dimensional optical orthogonal codes with weight 3 and different auto-and cross-correlation constraints by the authors recently.

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“…To overcome this problem, a two‐dimensional (2D) (constant‐weight) coding (also called multiwavelength CWOOCs) was introduced in . Recently many researchers are working on constructions and designs of 2D CWOOCs, see for some of the examples.…”

Section: Introductionmentioning

confidence: 99%

“…To overcome this problem, a twodimensional (2D) (constant-weight) coding (also called multiwavelength CWOOCs) was introduced in [37]. Recently many researchers are working on constructions and designs of 2D CWOOCs, see [6,7,13,21,[29][30][31][32] for some of the examples.In 1996, Yang introduced multimedia optical CDMA communication system employing variable-weight OOCs (1D VWOOC) [36]. In this CDMA system, the subscribers with different code weights will have different bit error rate (BER) performance.…”

mentioning

confidence: 99%

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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Semicyclic 4-GDDs and related two-dimensional optical orthogonal codes

Cited by 15 publications

References 27 publications

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

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

Semi-cyclic holey group divisible designs with block size three

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

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