{"title":"自正交码的多项式时间构造及其在量子纠错中的应用","authors":"M. Hamada","doi":"10.1109/ISIT.2009.5205647","DOIUrl":null,"url":null,"abstract":"A polynomial-time construction of a sequence of self-orthogonal geometric Goppa codes attaining the Tsfasman-Vlăduţ-Zink (TVZ) bound is presented. The issue of constructing such a code sequence was addressed in a context of constructing quantum error-correcting codes (Ashikhmin et al., 2001). Naturally, the obtained construction has implications on quantum error-correcting codes. In particular, the best known asymptotic lower bounds on the largest minimum distance of polynomially constructible quantum error-correcting codes are improved.","PeriodicalId":412925,"journal":{"name":"2009 IEEE International Symposium on Information Theory","volume":"23 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A polynomial-time construction of self-orthogonal codes and applications to quantum error correction\",\"authors\":\"M. Hamada\",\"doi\":\"10.1109/ISIT.2009.5205647\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A polynomial-time construction of a sequence of self-orthogonal geometric Goppa codes attaining the Tsfasman-Vlăduţ-Zink (TVZ) bound is presented. The issue of constructing such a code sequence was addressed in a context of constructing quantum error-correcting codes (Ashikhmin et al., 2001). Naturally, the obtained construction has implications on quantum error-correcting codes. In particular, the best known asymptotic lower bounds on the largest minimum distance of polynomially constructible quantum error-correcting codes are improved.\",\"PeriodicalId\":412925,\"journal\":{\"name\":\"2009 IEEE International Symposium on Information Theory\",\"volume\":\"23 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-06-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2009 IEEE International Symposium on Information Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISIT.2009.5205647\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 IEEE International Symposium on Information Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT.2009.5205647","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
给出了一组达到Tsfasman-Vlăduţ-Zink (TVZ)界的自正交几何Goppa码序列的多项式时间构造。构建这样一个代码序列的问题在构建量子纠错码的背景下得到了解决(Ashikhmin et al.， 2001)。自然地，所获得的结构对量子纠错码有影响。特别地，改进了多项式可构造量子纠错码的最大最小距离的已知渐近下界。
A polynomial-time construction of self-orthogonal codes and applications to quantum error correction
A polynomial-time construction of a sequence of self-orthogonal geometric Goppa codes attaining the Tsfasman-Vlăduţ-Zink (TVZ) bound is presented. The issue of constructing such a code sequence was addressed in a context of constructing quantum error-correcting codes (Ashikhmin et al., 2001). Naturally, the obtained construction has implications on quantum error-correcting codes. In particular, the best known asymptotic lower bounds on the largest minimum distance of polynomially constructible quantum error-correcting codes are improved.
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