用邻域搜索算法构造极值$ \mathbb{Z}_{4} $-码

IF 0.7 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Advances in Mathematics of Communications Pub Date : 2023-01-01 DOI:10.3934/amc.2023039

Dean Crnković, Matteo Mravić, Sanja Rukavina

{"title":"用邻域搜索算法构造极值$ \\mathbb{Z}_{4} $-码","authors":"Dean Crnković, Matteo Mravić, Sanja Rukavina","doi":"10.3934/amc.2023039","DOIUrl":null,"url":null,"abstract":"In this paper, we present a method for constructing extremal $ \\mathbb{Z}_{4} $-codes based on random neighborhood search. This method is used to find new extremal Type Ⅰ and Type Ⅱ $ \\mathbb{Z}_{4} $-codes of lengths 32 and 40. For the length 32, at least 182 new Type Ⅱ extremal $ \\mathbb{Z}_{4} $-codes of types $ 4^{k}2^{32-2k} $, $ k\\in\\left\\{9,10,12,13,14,15,16\\right\\} $ are constructed. In addition, we obtained at least 762 new extremal Type Ⅰ $ \\mathbb{Z}_{4} $-codes of types $ 4^{k}2^{32-2k} $, $ k\\in\\left\\{7,9,10,12,13,14,15,16\\right\\} $. For the length 40, constructed extremal $ \\mathbb{Z}_{4} $-codes are of types $ 4^{k}2^{40-2k} $, $ k\\in\\left\\{7,10,11,15,16\\right\\} $. There are at least 40 new Type Ⅱ extremal $ \\mathbb{Z}_{4} $-codes, and at least 4144 new Type Ⅰ extremal $ \\mathbb{Z}_{4} $-codes.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":"40 1","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Construction of extremal $ \\\\mathbb{Z}_{4} $-codes using a neighborhood search algorithm\",\"authors\":\"Dean Crnković, Matteo Mravić, Sanja Rukavina\",\"doi\":\"10.3934/amc.2023039\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we present a method for constructing extremal $ \\\\mathbb{Z}_{4} $-codes based on random neighborhood search. This method is used to find new extremal Type Ⅰ and Type Ⅱ $ \\\\mathbb{Z}_{4} $-codes of lengths 32 and 40. For the length 32, at least 182 new Type Ⅱ extremal $ \\\\mathbb{Z}_{4} $-codes of types $ 4^{k}2^{32-2k} $, $ k\\\\in\\\\left\\\\{9,10,12,13,14,15,16\\\\right\\\\} $ are constructed. In addition, we obtained at least 762 new extremal Type Ⅰ $ \\\\mathbb{Z}_{4} $-codes of types $ 4^{k}2^{32-2k} $, $ k\\\\in\\\\left\\\\{7,9,10,12,13,14,15,16\\\\right\\\\} $. For the length 40, constructed extremal $ \\\\mathbb{Z}_{4} $-codes are of types $ 4^{k}2^{40-2k} $, $ k\\\\in\\\\left\\\\{7,10,11,15,16\\\\right\\\\} $. There are at least 40 new Type Ⅱ extremal $ \\\\mathbb{Z}_{4} $-codes, and at least 4144 new Type Ⅰ extremal $ \\\\mathbb{Z}_{4} $-codes.\",\"PeriodicalId\":50859,\"journal\":{\"name\":\"Advances in Mathematics of Communications\",\"volume\":\"40 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Mathematics of Communications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/amc.2023039\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"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":"Advances in Mathematics of Communications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/amc.2023039","RegionNum":4,"RegionCategory":"计算机科学","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

本文提出了一种基于随机邻域搜索构造极值$ \mathbb{Z}_{4} $-码的方法。此方法用于查找新的极值类型Ⅰ和类型Ⅱ$ \mathbb{Z}_{4} $-长度为32和40的代码。对于长度32，至少构造182个新的类型Ⅱ极值$ \mathbb{Z}_{4} $-类型$ 4^{k}2^{32-2k} $， $ k\in\左\{9,10,12,13,14,15,16\右\}$的代码。此外，我们得到了至少762个新的极值类型Ⅰ$ \mathbb{Z}_{4} $-类型为$ 4^{k}2^{32-2k} $， $ k\ In \左\{7,9,10,12,13,14,15,16\右\}$的代码。对于长度40，构造的极值$ \mathbb{Z}_{4} $-代码的类型为$ 4^{k}2^{40-2k} $， $ k\in\左\{7,10,11,15,16\右\}$。至少有40个新的TypeⅡextremal $ \mathbb{Z}_{4} $-代码，以及至少4144个新的TypeⅠextremal $ \mathbb{Z}_{4} $-代码。

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

Construction of extremal $ \mathbb{Z}_{4} $-codes using a neighborhood search algorithm

In this paper, we present a method for constructing extremal $ \mathbb{Z}_{4} $-codes based on random neighborhood search. This method is used to find new extremal Type Ⅰ and Type Ⅱ $ \mathbb{Z}_{4} $-codes of lengths 32 and 40. For the length 32, at least 182 new Type Ⅱ extremal $ \mathbb{Z}_{4} $-codes of types $ 4^{k}2^{32-2k} $, $ k\in\left\{9,10,12,13,14,15,16\right\} $ are constructed. In addition, we obtained at least 762 new extremal Type Ⅰ $ \mathbb{Z}_{4} $-codes of types $ 4^{k}2^{32-2k} $, $ k\in\left\{7,9,10,12,13,14,15,16\right\} $. For the length 40, constructed extremal $ \mathbb{Z}_{4} $-codes are of types $ 4^{k}2^{40-2k} $, $ k\in\left\{7,10,11,15,16\right\} $. There are at least 40 new Type Ⅱ extremal $ \mathbb{Z}_{4} $-codes, and at least 4144 new Type Ⅰ extremal $ \mathbb{Z}_{4} $-codes.

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

Advances in Mathematics of Communications 工程技术-计算机：理论方法

CiteScore

2.20

自引率

22.20%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Mathematics of Communications (AMC) publishes original research papers of the highest quality in all areas of mathematics and computer science which are relevant to applications in communications technology. For this reason, submissions from many areas of mathematics are invited, provided these show a high level of originality, new techniques, an innovative approach, novel methodologies, or otherwise a high level of depth and sophistication. Any work that does not conform to these standards will be rejected. Areas covered include coding theory, cryptology, combinatorics, finite geometry, algebra and number theory, but are not restricted to these. This journal also aims to cover the algorithmic and computational aspects of these disciplines. Hence, all mathematics and computer science contributions of appropriate depth and relevance to the above mentioned applications in communications technology are welcome. More detailed indication of the journal''s scope is given by the subject interests of the members of the board of editors.