Determination of the sizes of optimal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mrow><mml:mo>(</mml:mo><mml:mi>m</mml:mi><mml:mo>,</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>λ</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-OOSPCs for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" display="inl

Pan, Rong; Chang, Yanxun

doi:10.1016/j.disc.2013.02.019

Cited by 9 publications

(4 citation statements)

References 6 publications

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“…Multipleweight (MW) OOSPCs were introduced by Kwong and Yang to meet multiple quality of services (QoS) requirement [23]. For OOSPCs and MW-OOSPCs, the interested readers may refer to [12], [13], [20], [22], [24], [27], [28], [29], [30], [31], [32], [36], [38] and the references therein.…”

Section: Application To Oospcsmentioning

confidence: 99%

“…(u, v, g, h) =(2,108,2,12) {(0,0),(0,65),(0,89),(1,52)}, {(0,0),(0,5),(0,37), (1,43),(1,49)}, {(0,0),(0,30),(0,47),(0,68)}, {(0,0),(0,59),(0,60),(0,93),(1,91)}, {(0,0),(0,10),(0,52),(0,83),(1,33)}, {(0,0),(0,46),(0,96), (1,35), (1,39)}, {(0,0),(0,3),(0,23), (1,28),(1,107)}, {(0,0),(0,13), (1,53),(1,92)}, {(0,0),(0,8),(0,22),(1,30)}, {(0,0),(0,51),(0,67),(1,93)}, {(0,0),(0,7), (1,10), (1,21),(1,74)}, {(0,0),(0,2),(0,28),(1,48)}.…”

mentioning

confidence: 99%

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On balanced $(Z_{4u}\times Z_{8v},\{4,5\},1)$ difference packings

Zhao¹,

Qin²,

Wu³

2021

Preprint

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Let K be a set of positive integers and let G be an additive group. A (G, K, 1) difference packing is a set of subsets of G with sizes from K whose list of differences covers every element of G at most once. It is balanced if the number of blocks of size k ∈ K does not depend on k. In this paper, we determine a balanced (Z 4u × Z 8v , 4, 5, 1) difference packing of the largest possible size whenever uv is odd. The corresponding optimal balanced (4u, 8v, {4, 5}, 1) optical orthogonal signature pattern codes are also obtained.

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Section: Application To Oospcsmentioning

confidence: 99%

mentioning

confidence: 99%

On balanced $(Z_{4u}\times Z_{8v},\{4,5\},1)$ difference packings

Zhao¹,

Qin²,

Wu³

2021

Preprint

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show abstract

“…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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“…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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Determination of the sizes of optimal (m,n,k,λ,k−1)-OOSPCs for
Rong Pan
¹
,
Yanxun Chang
²

Cited by 9 publications

References 6 publications

On balanced $(Z_{4u}\times Z_{8v},\{4,5\},1)$ difference packings

On balanced $(Z_{4u}\times Z_{8v},\{4,5\},1)$ difference packings

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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Determination of the sizes of optimal (m,n,k,λ,k−1)-OOSPCs for Rong Pan1, Yanxun Chang2

Cited by 9 publications

References 6 publications

On balanced $(Z_{4u}\times Z_{8v},\{4,5\},1)$ difference packings

On balanced $(Z_{4u}\times Z_{8v},\{4,5\},1)$ difference packings

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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Determination of the sizes of optimal (m,n,k,λ,k−1)-OOSPCs for
Rong Pan
¹
,
Yanxun Chang
²