{"title":"构建 AEAQEC 代码的新方法","authors":"Peng Hu , Xiusheng Liu","doi":"10.1016/j.disc.2024.114202","DOIUrl":null,"url":null,"abstract":"<div><p>Recently, Liu and Liu gave the Singleton bound for pure asymmetric entanglement-assisted quantum error-correcting (AEAQEC) codes. They constructed three new families of AQEAEC codes by means of Vandermonde matrices, generalized Reed-Solomon (GRS) codes and cyclic codes. In this paper, we first exhibit the Singleton bound for any AEAQEC codes. Then we construct AEAQEC codes by two distinct constacyclic codes. By means of repeated-root cyclic codes, we construct new AEAQEC MDS codes. In addition, our methods allow for easily calculating the dimensions, <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>z</mi></mrow></msub></math></span>, <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span> and the number <em>c</em> of pre-shared maximally entangled states of AEAQEC codes.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"New methods for constructing AEAQEC codes\",\"authors\":\"Peng Hu , Xiusheng Liu\",\"doi\":\"10.1016/j.disc.2024.114202\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Recently, Liu and Liu gave the Singleton bound for pure asymmetric entanglement-assisted quantum error-correcting (AEAQEC) codes. They constructed three new families of AQEAEC codes by means of Vandermonde matrices, generalized Reed-Solomon (GRS) codes and cyclic codes. In this paper, we first exhibit the Singleton bound for any AEAQEC codes. Then we construct AEAQEC codes by two distinct constacyclic codes. By means of repeated-root cyclic codes, we construct new AEAQEC MDS codes. In addition, our methods allow for easily calculating the dimensions, <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>z</mi></mrow></msub></math></span>, <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span> and the number <em>c</em> of pre-shared maximally entangled states of AEAQEC codes.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-08-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0012365X24003339\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X24003339","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Recently, Liu and Liu gave the Singleton bound for pure asymmetric entanglement-assisted quantum error-correcting (AEAQEC) codes. They constructed three new families of AQEAEC codes by means of Vandermonde matrices, generalized Reed-Solomon (GRS) codes and cyclic codes. In this paper, we first exhibit the Singleton bound for any AEAQEC codes. Then we construct AEAQEC codes by two distinct constacyclic codes. By means of repeated-root cyclic codes, we construct new AEAQEC MDS codes. In addition, our methods allow for easily calculating the dimensions, , and the number c of pre-shared maximally entangled states of AEAQEC codes.
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