{"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}
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.
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.