$(m\kern -1pt,n\kern -1pt,3\kern -1pt,1)$  Optical Orthogonal Signature Pattern Codes With Maximum Possible Size

Pan, Rong; Chang, Yanxun

doi:10.1109/tit.2014.2381259

Cited by 23 publications

(12 citation statements)

References 28 publications

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“…For more details, the interested readers may refer to [22,23,30]. And the results about OOSPCs, the interested readers may refer to [13,14,25,27,29] and the reference therein.…”

Section: Optimal G ( 4 1)-dp and Oospcsmentioning

confidence: 99%

“…m n ( , ) = (6, 36): {(0, 0), (5,30), (1, 0), (1, 28)}, {(0, 0), (0, 4), (1,8), (1,25)}, {(0, 0), (5,35), (2,13), (2, 14)}, {(0, 0), (5,31), (5,17), (2, 26)}, {(0, 0), (1,30), (2,11), (3, 10)}, {(0, 0), (5,29), (5,3), (2, 28)}, {(0, 0), (1,22), (0, 27), (0, 2)}, {(0, 0), (5,34), (1,27), (3,29)}, {(0, 0), (1,24), (0, 13), (2, 0)}, {(0, 0), (1,26), (0, 16), (2, 4)}, {(0, 0), (4,16), (0, 33), (2, 7)}, {(0, 0), (5,20), (2,12), (2, 33)}, {(0, 0), (1,13), (2,31), (5,27)}, {(0, 0), (5,7), (4,…”

Section: Appendix Bmentioning

confidence: 99%

“…The reader can refer to [1,3,[6][7][8]10,31,32] on mn k ( , , 1)-DPs. When m and n are not coprime, to our knowledge the existence of an optimal m n k ( × , , 1)-DP has not been much investigated, the reader can refer to [25][26][27] and the reference therein.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On optimal (Z6m×Z6n,4,1) and (Z2m×Z18n,4,1) difference packings and their related codes

Chen

2021

J of Combinatorial Designs

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“…For more details, the interested readers may refer to [22,23,30]. And the results about OOSPCs, the interested readers may refer to [13,14,25,27,29] and the reference therein.…”

Section: Optimal G ( 4 1)-dp and Oospcsmentioning

confidence: 99%

Section: Appendix Bmentioning

confidence: 99%

See 1 more Smart Citation

On optimal (Z6m×Z6n,4,1) and (Z2m×Z18n,4,1) difference packings and their related codes

Chen

2021

J of Combinatorial Designs

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“…Multiple-weight (MW) OOSPCs were introduced by Kwong and Yang to meet multiple quality of services (QoS) requirement [25]. For OOSPCs and MW-OOSPCs, the interested readers may refer to [13], [14], [22], [24], [26], [29], [30], [31], [32], [33], [35], [36], [40], [44] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Balanced ($\mathbb{Z} _{2u}\times \mathbb{Z}_{38v}$, {3, 4, 5}, 1) difference packings and related codes

Zhao¹,

Qin²,

Wu³

2024

AMC

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<p style='text-indent:20px;'>Let <inline-formula><tex-math id="M1">\begin{document}$ m $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ n $\end{document}</tex-math></inline-formula> be positive integers, and <inline-formula><tex-math id="M3">\begin{document}$ K $\end{document}</tex-math></inline-formula> a set of positive integers with size greater than 2. An <inline-formula><tex-math id="M4">\begin{document}$ (m,n,K,1) $\end{document}</tex-math></inline-formula> optical orthogonal signature pattern code, <inline-formula><tex-math id="M5">\begin{document}$ (m,n,K,1) $\end{document}</tex-math></inline-formula>-OOSPC, was introduced by Kwong and Yang for 2-D image transmission in multicore-fiber optical code-division multiple-access (OCDMA) networks with multiple quality of services (QoS) requirement. Let <inline-formula><tex-math id="M6">\begin{document}$ G $\end{document}</tex-math></inline-formula> be an additive group, a balanced <inline-formula><tex-math id="M7">\begin{document}$ (G, K, 1) $\end{document}</tex-math></inline-formula> difference packing, <inline-formula><tex-math id="M8">\begin{document}$ (G, K, 1) $\end{document}</tex-math></inline-formula>-BDP, can be used to construct a balanced <inline-formula><tex-math id="M9">\begin{document}$ (m,n,K,1) $\end{document}</tex-math></inline-formula>-OOSPC when <inline-formula><tex-math id="M10">\begin{document}$ G = {\mathbb{Z}}_m\times {\mathbb{Z}}_n $\end{document}</tex-math></inline-formula>. In this paper, the existences of optimal <inline-formula><tex-math id="M11">\begin{document}$ ( {\mathbb{Z}}_{2u}\times {\mathbb{Z}}_{38v}, \{3,4,5\},1) $\end{document}</tex-math></inline-formula>-BDPs are completely solved with <inline-formula><tex-math id="M12">\begin{document}$ u, \ v\equiv 1\pmod2 $\end{document}</tex-math></inline-formula>, and the corresponding optimal balanced <inline-formula><tex-math id="M13">\begin{document}$ (2u, 38v,\{3,4,5\},1) $\end{document}</tex-math></inline-formula>-OOSPCs are also obtained.</p>

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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%

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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$(m\kern -1pt,n\kern -1pt,3\kern -1pt,1)$ Optical Orthogonal Signature Pattern Codes With Maximum Possible Size

Cited by 23 publications

References 28 publications

On optimal (Z6m×Z6n,4,1) and (Z2m×Z18n,4,1) difference packings and their related codes

On optimal (Z6m×Z6n,4,1) and (Z2m×Z18n,4,1) difference packings and their related codes

Balanced ($\mathbb{Z} _{2u}\times \mathbb{Z}_{38v}$, {3, 4, 5}, 1) difference packings and related codes

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

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