循环外部差异族：构建与不存在

IF 1.4 2区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Designs, Codes and Cryptography Pub Date : 2024-06-12 DOI:10.1007/s10623-024-01443-5

Huawei Wu, Jing Yang, Keqin Feng

{"title":"循环外部差异族：构建与不存在","authors":"Huawei Wu, Jing Yang, Keqin Feng","doi":"10.1007/s10623-024-01443-5","DOIUrl":null,"url":null,"abstract":"<p>The circular external difference family and its strong version are of great significance both in theory and in applications. In this paper, we apply the classical cyclotomic construction to the circular external differnece family and exhibit several concrete examples, in particular constructing an infinite family. Furthermore, we prove that all strong circular external differnece families are constructed by patching together several strong external difference families consisting of two subsets, thereby solving the open problem raised by Veitch and Stinson. We also present a new result on the non-existence of a certain type of strong external difference families.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":null,"pages":null},"PeriodicalIF":1.4000,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Circular external difference families: construction and non-existence\",\"authors\":\"Huawei Wu, Jing Yang, Keqin Feng\",\"doi\":\"10.1007/s10623-024-01443-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The circular external difference family and its strong version are of great significance both in theory and in applications. In this paper, we apply the classical cyclotomic construction to the circular external differnece family and exhibit several concrete examples, in particular constructing an infinite family. Furthermore, we prove that all strong circular external differnece families are constructed by patching together several strong external difference families consisting of two subsets, thereby solving the open problem raised by Veitch and Stinson. We also present a new result on the non-existence of a certain type of strong external difference families.</p>\",\"PeriodicalId\":11130,\"journal\":{\"name\":\"Designs, Codes and Cryptography\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-06-12\",\"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/s10623-024-01443-5\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Designs, Codes and Cryptography","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10623-024-01443-5","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

摘要

圆周外差族及其强序列在理论和应用方面都具有重要意义。在本文中，我们将经典的循环构造应用于圆外差族，并展示了几个具体的例子，特别是构造了一个无穷族。此外，我们还证明了所有强循环外差族都是由两个子集组成的几个强外差族拼凑而成的，从而解决了维奇和斯坦森提出的未决问题。我们还提出了关于某类强外差族不存在的新结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Circular external difference families: construction and non-existence

The circular external difference family and its strong version are of great significance both in theory and in applications. In this paper, we apply the classical cyclotomic construction to the circular external differnece family and exhibit several concrete examples, in particular constructing an infinite family. Furthermore, we prove that all strong circular external differnece families are constructed by patching together several strong external difference families consisting of two subsets, thereby solving the open problem raised by Veitch and Stinson. We also present a new result on the non-existence of a certain type of strong external difference families.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Designs, Codes and Cryptography 工程技术-计算机：理论方法

CiteScore

2.80

自引率

12.50%

发文量

157

审稿时长

16.5 months

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.