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<p>Two-dimensional multilength optical orthogonal codes (2D MLOOCs) were proposed as a means of simultaneously reducing the chip rate and accommodating multimedia services with multiple bit rates and quality of service (QoS) requirements in OCDMA networks. This paper considers two-dimensional multilength optical orthogonal codes with inter-cross-correlation of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10623_2025_1587_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\(\lambda =2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>λ</mi> <mo>=</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. New upper bounds on the size of 2D MLOOCs are presented under certain constraints. In order to construct optimal 2D MLOOCs, a compatible mixed difference packing (CMDP) set system is introduced. By using both direct constructions and recursive constructions, several series of 2D MLOOCs are obtained which are optimal with respect to the new upper bounds.</p>

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Optimal two-dimensional multilength optical orthogonal codes via compatible mixed difference packing set systems

  • 期刊论文

  • 发表日期：

    2025年2月18日

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  • Hengming Zhao,
  • Rongcun Qin,
  • Minquan Cheng,
  • Dianhua Wu

摘要

Two-dimensional multilength optical orthogonal codes (2D MLOOCs) were proposed as a means of simultaneously reducing the chip rate and accommodating multimedia services with multiple bit rates and quality of service (QoS) requirements in OCDMA networks. This paper considers two-dimensional multilength optical orthogonal codes with inter-cross-correlation of \(\lambda =2\) λ = 2 . New upper bounds on the size of 2D MLOOCs are presented under certain constraints. In order to construct optimal 2D MLOOCs, a compatible mixed difference packing (CMDP) set system is introduced. By using both direct constructions and recursive constructions, several series of 2D MLOOCs are obtained which are optimal with respect to the new upper bounds.