通过矩阵积编码构建 AEAQEC 编码

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-07-26 DOI:10.1016/j.disc.2024.114184

{"title":"通过矩阵积编码构建 AEAQEC 编码","authors":"","doi":"10.1016/j.disc.2024.114184","DOIUrl":null,"url":null,"abstract":"<div><p>Recently, Galindo et al. introduced the concept of asymmetric entanglement-assisted quantum error-correcting (AEAQEC, for short) code, and gave some good AEAQEC codes. In this paper, we provide two methods of constructing AEAQEC codes by means of two matrix-product codes from constacyclic codes over finite fields. The first one is derived from the rank of a relationship of generator matrices based on two matrix-product codes. The second construction is derived from the dimension of intersection for two matrix-product codes. By means of these methods, concrete examples are presented to construct new AEAQEC codes. In addition, our obtained AEQAEC codes have better parameters than the ones available in the literature.</p></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Constructions of AEAQEC codes via matrix-product codes\",\"authors\":\"\",\"doi\":\"10.1016/j.disc.2024.114184\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Recently, Galindo et al. introduced the concept of asymmetric entanglement-assisted quantum error-correcting (AEAQEC, for short) code, and gave some good AEAQEC codes. In this paper, we provide two methods of constructing AEAQEC codes by means of two matrix-product codes from constacyclic codes over finite fields. The first one is derived from the rank of a relationship of generator matrices based on two matrix-product codes. The second construction is derived from the dimension of intersection for two matrix-product codes. By means of these methods, concrete examples are presented to construct new AEAQEC codes. In addition, our obtained AEQAEC codes have better parameters than the ones available in the literature.</p></div>\",\"PeriodicalId\":50572,\"journal\":{\"name\":\"Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-07-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0012365X24003157\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X24003157","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

最近，Galindo 等人提出了非对称纠缠辅助量子纠错码（简称 AEAQEC）的概念，并给出了一些很好的 AEAQEC 码。在本文中，我们提供了两种通过有限域上的常簇码的两个矩阵积码来构造 AEAQEC 码的方法。第一种方法是从基于两个矩阵-乘积码的生成矩阵关系的秩推导出来的。第二个构造是从两个矩阵-乘积码的交集维度推导出来的。通过这些方法，提出了构建新的 AEAQEC 代码的具体实例。此外，我们获得的 AEQAEC 代码的参数优于现有文献。

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

Constructions of AEAQEC codes via matrix-product codes

Recently, Galindo et al. introduced the concept of asymmetric entanglement-assisted quantum error-correcting (AEAQEC, for short) code, and gave some good AEAQEC codes. In this paper, we provide two methods of constructing AEAQEC codes by means of two matrix-product codes from constacyclic codes over finite fields. The first one is derived from the rank of a relationship of generator matrices based on two matrix-product codes. The second construction is derived from the dimension of intersection for two matrix-product codes. By means of these methods, concrete examples are presented to construct new AEAQEC codes. In addition, our obtained AEQAEC codes have better parameters than the ones available in the literature.

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

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.