New optical orthogonal signature pattern codes with maximum collision parameter 2 and weight 4

Chen, Jingyuan; Ji, Lijun; Li, Yun

doi:10.1007/s10623-016-0310-8

Cited by 12 publications

(23 citation statements)

References 30 publications

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“…When u and v are not coprime, the construction of optimal (u, v, k, λ a , λ c )-OOSPCs becomes difficult. For k = 3, 4, some results have been obtained for optimal (u, v, k, λ a , λ c )-OOSPCs [5], [6], [20], [22], [23], [19], [27], [28]. For general weight k, some results on (asymptotically ) optimal (u, v, k, λ a , λ c )-OOSPCs are also obtained [14], [21], [32].…”

Section: Introductionmentioning

confidence: 99%

“…It was proposed by Kwong and Yang for OCDMA networks to support multiple quality of services (QoS) [18]. We will give the definition of a multiple-weight optical orthogonal signature pattern code from set-point of view as done in [6], [20], [27].…”

Section: Introductionmentioning

confidence: 99%

“…There exists a balanced (u × v, g × h, {4, 5}, 1)-SP for (u, v, g, h) = (2, 144, 2, 16), (3, 24, 1, 8), (3, 72, 1, 24), (9, 24, 1, 24),(6, 48,2,16).…”

mentioning

confidence: 99%

“…-SP exists from Lemma 4.7, where (g, h) = (2, 16), (2, 48), (6,16). For (g, h) = (2, 16), the SP is optimal.…”

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confidence: 99%

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Constructions of optimal balanced $ (m, n, \{4, 5\}, 1) $-OOSPCs

Li¹,

Zhao²,

Qin³

et al. 2019

Advances in Mathematics of Communications

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Kitayama proposed a novel OCDMA (called spatial CDMA) for parallel transmission of 2-D images through multicore fiber. Optical orthogonal signature pattern codes (OOSPCs) play an important role in this CDMA network. Multiple-weight (MW) optical orthogonal signature pattern code (OOSPC) was introduced by Kwong and Yang for 2-D image transmission in multicore-fiber optical code-division multiple-access (OCDMA) networks with multiple quality of services (QoS) requirements. Some results had been done on optimal balanced (m, n, {3, 4}, 1)-OOSPCs. In this paper, it is proved that there exist optimal balanced (2u, 16v, {4, 5}, 1)-OOSPCs for odd integers u ≥ 1, v ≥ 1.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Constructions of optimal balanced $ (m, n, \{4, 5\}, 1) $-OOSPCs

Li¹,

Zhao²,

Qin³

et al. 2019

Advances in Mathematics of Communications

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“…The exact number of codewords of an optimal (m, n, 3, λ a , 1)-OOSPC is determined for any positive integers m, n ≡ 2 (mod 4) and λ a ∈ {2, 3}.When m and n are coprime, it has been shown in [28] that an (m, n, k, λ a , λ c )-OOSPC is equivalent to a 1-dimensional (mn, k, λ a , λ c )-optical orthogonal code (OOC). See [1-4, 7, 10, 13, 14, 29] and the references therein for more details on OOCs.When m and n are not coprime, various OOSPCs have been constructed via algebraic and combinatorial methods for the case of λ a = λ c (see [5,6,15,[23][24][25][26]28]). We only quote the following result for later use.…”

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confidence: 99%

Optimal optical orthogonal signature pattern codes with weight three and cross-correlation constraint one

Pan

Feng

Wang³

et al. 2019

Des. Codes Cryptogr.

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Optical orthogonal signature pattern codes (OOSPCs) have attracted wide attention as signature patterns of spatial optical code division multiple access networks. In this paper, an improved upper bound on the size of an (m, n, 3, λ a , 1)-OOSPC with λ a = 2, 3 is established. The exact number of codewords of an optimal (m, n, 3, λ a , 1)-OOSPC is determined for any positive integers m, n ≡ 2 (mod 4) and λ a ∈ {2, 3}.When m and n are coprime, it has been shown in [28] that an (m, n, k, λ a , λ c )-OOSPC is equivalent to a 1-dimensional (mn, k, λ a , λ c )-optical orthogonal code (OOC). See [1-4, 7, 10, 13, 14, 29] and the references therein for more details on OOCs.When m and n are not coprime, various OOSPCs have been constructed via algebraic and combinatorial methods for the case of λ a = λ c (see [5,6,15,[23][24][25][26]28]). We only quote the following result for later use. Theorem 1.1 [24] Θ(m, n, 3, 1) =              J(mn, 3, 1) − 1, if mn ≡ 14, 20 (mod 24), or if mn ≡ 8, 16 (mod 24) and gcd(m, n, 4) = 2, or if mn ≡ 2 (mod 6) and gcd(m, n, 4) = 4; J(mn, 3, 1), otherwise.On the other hand, for the case of λ a = λ c , very little has been done on (m, n, k, λ a , λ c )-OOSPCs with maximum size. Compared with (1.1), an improved upper bound on Θ(m, n, 3, 2, 1) was given by Sawa and Kageyama [26]. That is Θ(m, n, 3, 2, 1) ≤ mn 4 , if mn ≡ 0 (mod 4), mn−1 4 , otherwise.(1.2)And they proved the following theorem. Theorem 1.2 [26] Θ(m, n, 3, 2, 1) = mn−1 4 , if m = n ≡ 1 (mod 4) is a prime and 2 is a primitive root in Z m ; mn−2 4 , if mn ≡ 2 (mod 4).In Section 2, we shall give an equivalent combinatorial description of (m, n, k, λ a , λ c )-OOSPCs by using set-theoretic notation. Section 3 is devoted to improving Sawa and Kageyama's bound (1.2), especially for the case of mn ≡ 0 (mod 4). Throughout this paper, let ξ denote the number of subgroups of order 3 in Z m × Z n , i.e., ξ =    0, if 3 ∤ mn; 1, if 3 | mn and gcd(m, n, 3) = 1; 4, if gcd(m, n, 3) = 3.

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