{"title":"New quantum codes from constacyclic codes over finite chain rings","authors":"Yongsheng Tang, Ting Yao, Heqian Xu, Xiaoshan Kai","doi":"10.1007/s11128-024-04519-2","DOIUrl":null,"url":null,"abstract":"<div><p>Let <i>R</i> be the finite chain ring <span>\\(\\mathbb {F}_{p^{2m}}+{u}\\mathbb {F}_{p^{2m}}\\)</span>, where <span>\\(\\mathbb {F}_{p^{2m}}\\)</span> is the finite field with <span>\\(p^{2m}\\)</span> elements, <i>p</i> is a prime, <i>m</i> is a non-negative integer and <span>\\({u}^{2}=0.\\)</span> In this paper, we firstly define a class of Gray maps, which changes the Hermitian self-orthogonal property of linear codes over <span>\\(\\mathbb {F}_{2^{2m}}+{u}\\mathbb {F}_{2^{2m}}\\)</span> into the Hermitian self-orthogonal property of linear codes over <span>\\(\\mathbb {F}_{2^{2m}}\\)</span>. Applying the Hermitian construction, a new class of <span>\\(2^{m}\\)</span>-ary quantum codes are obtained from Hermitian constacyclic self-orthogonal codes over <span>\\(\\mathbb {F}_{2^{2m}}+{u}\\mathbb {F}_{2^{2m}}.\\)</span> We secondly define another class of maps, which changes the Hermitian self-orthogonal property of linear codes over <i>R</i> into the trace self-orthogonal property of linear codes over <span>\\(\\mathbb {F}_{p^{2m}}\\)</span>. Using the Symplectic construction, a new class of <span>\\(p^{m}\\)</span>-ary quantum codes are obtained from Hermitian constacyclic self-orthogonal codes over <i>R</i>.</p></div>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Information Processing","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11128-024-04519-2","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Let R be the finite chain ring \(\mathbb {F}_{p^{2m}}+{u}\mathbb {F}_{p^{2m}}\), where \(\mathbb {F}_{p^{2m}}\) is the finite field with \(p^{2m}\) elements, p is a prime, m is a non-negative integer and \({u}^{2}=0.\) In this paper, we firstly define a class of Gray maps, which changes the Hermitian self-orthogonal property of linear codes over \(\mathbb {F}_{2^{2m}}+{u}\mathbb {F}_{2^{2m}}\) into the Hermitian self-orthogonal property of linear codes over \(\mathbb {F}_{2^{2m}}\). Applying the Hermitian construction, a new class of \(2^{m}\)-ary quantum codes are obtained from Hermitian constacyclic self-orthogonal codes over \(\mathbb {F}_{2^{2m}}+{u}\mathbb {F}_{2^{2m}}.\) We secondly define another class of maps, which changes the Hermitian self-orthogonal property of linear codes over R into the trace self-orthogonal property of linear codes over \(\mathbb {F}_{p^{2m}}\). Using the Symplectic construction, a new class of \(p^{m}\)-ary quantum codes are obtained from Hermitian constacyclic self-orthogonal codes over R.
期刊介绍:
Quantum Information Processing is a high-impact, international journal publishing cutting-edge experimental and theoretical research in all areas of Quantum Information Science. Topics of interest include quantum cryptography and communications, entanglement and discord, quantum algorithms, quantum error correction and fault tolerance, quantum computer science, quantum imaging and sensing, and experimental platforms for quantum information. Quantum Information Processing supports and inspires research by providing a comprehensive peer review process, and broadcasting high quality results in a range of formats. These include original papers, letters, broadly focused perspectives, comprehensive review articles, book reviews, and special topical issues. The journal is particularly interested in papers detailing and demonstrating quantum information protocols for cryptography, communications, computation, and sensing.