{"title":"Optimal two-dimensional multilength optical orthogonal codes via compatible mixed difference packing set systems","authors":"Hengming Zhao, Rongcun Qin, Minquan Cheng, Dianhua Wu","doi":"10.1007/s10623-025-01587-y","DOIUrl":null,"url":null,"abstract":"<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 <span>\\(\\lambda =2\\)</span>. 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>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"24 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Designs, Codes and Cryptography","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10623-025-01587-y","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
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 \(\lambda =2\). 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.
期刊介绍：
Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines.
The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome.
The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas.
Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.
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