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International Conference on Web Information Systems and Mining

作者： Zhong, Shuqin Ma, Zhi Zhengzhou Informat Sci & Technol Inst Zhengzhou 450002 Peoples R China

ISBN: (纸本)9780769538174

This paper studied the construction for quantum code with parameters ((n, K, d)), by use of an n-variable logic function with APC distance d' >= 2 over F-p. We discussed the parameters of the constructed quantum codes, then obtained d <= d' and the maximal K for all d = d'-k, 0 <= k <= d'-2. It was also discussed the basic states and the equivalent conditions of meeting quantum Singleton bound in this paper. With our result, for a given function wit APC distance d' >= 2, we can construct quantum codes with the minimum distance d = d'-k for all 0 <= k <= d' - 2 and presented the basic states of the constructed codes.

关键词： quantum code logic state logic function

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On a construction of a nonstabilizer Clifford quantum code for 2h(2j+1)-level states

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ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE 2007年第4期90卷 63-68页

作者： Hagiwara, Manabu Imai, Hideki Natl Inst Adv Ind Sci & Technol Tokyo 1010021 Japan Univ Tokyo Inst Ind Sci Tokyo 1538505 Japan

The construction of an infinite number of nonstabilizer codes of Clifford type was given for the first tithe by the authors. However, the method of construction was restricted to encoding from odd prime p-level quantum states to 2p-level states. In this paper, the result is extended to the construction of nonstabilizer-type quantum codes which encode quantum states of arbitrary odd 2j+1-level to quantum states of 2h(2j+1)-level, where h are mutually prime 2j+1. (C) 2006 Wiley Periodicals, Inc.

关键词： quantum code Clifford code stabilizer code

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The Nonexistence of a []-quantum Stabilizer code

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IEEE TRANSACTIONS ON INFORMATION THEORY 2011年第7期57卷 4788-4793页

作者： Bierbrauer, Juergen Fears, Richard Marcugini, Stefano Pambianco, Fernanda Michigan Technol Univ Dept Math Sci Houghton MI 49931 USA Univ Perugia Dipartimento Matemat & Informat I-06100 Perugia Italy

One of the oldest problems in the theory of quantum stabilizer codes is solved by proving the nonexistence of quantum [[13, 5, 4]]-codes.

关键词： Additive code codeline dimension hyperplane quantum code stabilizer code strength symplectic geometry weight

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Additive twisted codes: new distance bounds and infinite families of quantum codes

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DESIGNS codeS AND CRYPTOGRAPHY 2025年 1-38页

作者： Dastbasteh, Reza Lisonek, Petr Tecnun Univ Navarra Donostia San Sebastian Spain Simon Fraser Univ Dept Math Burnaby BC Canada

We provide a new construction of quantum codes that enables integration of a broader class of classical codes into the mathematical framework of quantum stabilizer codes. Next, we present new connections between twisted codes and linear cyclic codes and provide novel bounds for the minimum distance of twisted codes. We show that classical tools such as the Hartmann-Tzeng minimum distance bound are applicable to twisted codes. This enabled us to discover five new infinite families and many other examples of record-breaking, and sometimes optimal, binary quantum codes. We also discuss the role of the gamma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document} value on the parameters of twisted codes and present new results regarding the construction of twisted codes with different gamma\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma $$\end{document} values but identical parameters. Finally, we list many new record-breaking binary quantum codes that we obtained from additive twisted, linear cyclic, and constacyclic codes.

关键词： Additive code Twisted code Cyclic code quantum code Minimum distance bound

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Bounds and Constructions of quantum Locally Recoverable codes From quantum CSS codes

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IEEE TRANSACTIONS ON INFORMATION THEORY 2025年第3期71卷 1794-1802页

作者： Luo, Gaojun Chen, Bocong Ezerman, Martianus Frederic Ling, San Nanjing Univ Aeronaut & Astronaut Sch Math Nanjing 211106 Jiangsu Peoples R China Nanyang Technol Univ Sch Phys & Math Sci Singapore 637371 Singapore South China Univ Technol Sch Future Technol Guangzhou 510641 Peoples R China PQStn Singapore 408564 Singapore

Classical locally recoverable codes (LRCs) have become indispensable in distributed storage systems. They provide efficient recovery in terms of localized errors. quantum LRCs have very recently been introduced for their potential application in quantum data storage. In this paper, we use classical LRCs to investigate quantum LRCs. We prove that the parameters of quantum LRCs are bounded by their classical counterparts. We deduce bounds on the parameters of quantum LRCs from bounds on the parameters of the classical ones. We establish a characterization of optimal pure quantum LRCs based on classical codes with specific properties. Using well-crafted classical LRCs as ingredients in the construction of quantum CSS codes, we offer the first construction of several families of optimal pure quantum LRCs.

关键词： codes Linear codes Systematics Symbols Parity check codes Memory Hamming weight Finite element analysis codecs Vectors CSS code locally recoverable code quantum code

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quantum codes from Constacyclic codes over Polynomial Residue Rings

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Chinese Journal of Electronics 2019年第6期28卷 1131-1138页

作者： DING Jian LI Hongju LIANG Jing TANG Yongsheng College of Mathematics and Informatics Fujian Normal University Fujian Provincial Key Lab of Network Security and Cryptology Fujian Normal University Department of General Education Anhui Xinhua University School of Mathematics and Statistics Hefei Normal University

Sufficient and necessary conditions for Hermitian（1 + λu）-constacyclic self-orthogonal codes over F;m +uF;m are obtained, where λ is a unit of F;m +uF;*** on this, a new method for the construction of p;ary quantum codes from the obtained Hermitian（1 + λu）-constacyclic self-orthogonal codes over F;m +uF;m is *** an example, [[p;-1, p;-2d + 1, d]];m quantum MDS codes are constructed for 1 ≤ d ≤（p;+ 1）/2 and p ≠ 2, as well as some other quantum codes.

关键词： quantum code quantum MDS code Constacyclic code Self-orthogonal code

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quantum codes from the cyclic codes over Fp[u, v, w]/⟨u²-1, v²-1, w²-1, uv - vu, vw - wv, wu - uw⟩

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2019年第1-2期60卷 625-635页

作者： Islam, Habibul Prakash, Om Indian Inst Technol Patna Dept Math Patna 801106 Bihar India

In this article, for any odd prime p, we construct the quantum codes over Fp by using the cyclic codes of length n over R=Fp[u,v,w]/u2-1,v2-1,w2-1,uv-vu,vw-wv,wu-uw. We obtain the self-orthogonal properties of cyclic ... 详细信息

关键词： Cyclic code quantum code Gray map Self-orthogonal code

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quantum codes Derived From Certain Classes of Polynomials

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IEEE TRANSACTIONS ON INFORMATION THEORY 2016年第11期62卷 6638-6643页

作者： Zhang, Tao Ge, Gennian Capital Normal Univ Sch Math Sci Beijing 100048 Peoples R China Zhejiang Univ Sch Math Sci Hangzhou 310027 Zhejiang Peoples R China Beijing Ctr Math & Informat Interdisciplinary Sci Beijing 100048 Peoples R China

One central theme in quantum error-correction is to construct quantum codes that have a relatively large minimum distance. In this paper, we first present a construction of classical linear codes based on certain classes of polynomials. Through these classical linear codes, we are able to obtain some new quantum codes. It turns out that some of the quantum codes exhibited here have better parameters than the ones available in the literature.

关键词： quantum code polynomial code cyclotomic coset

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quantum codes from one-point codes on norm-trace curves

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CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES 2022年第5期14卷 1179-1188页

作者： Kim, Boran Kyungpook Natl Univ Dept Math Educ Teachers Coll 80 Daehakro Daegu 41566 South Korea

In this paper, we present quantum codes via algebraic geometry codes on norm-trace curves. We provide a lower bound of minimum Hamming distance for q-ary quantum code, where q = 2(e) (e >= 3). In order to get this, we determine Feng-Rao function values for the elements of Weierstrass semigroups on norm-trace curves. We present the order-bound on the minimum Hamming distance of one-point dual codes. Furthermore, we give a certain increasing sequence of one-point codes on norm-trace curves. We construct quantum codes from the sequence of one-point codes via the CSS construction. These give a better lower bound on the minimum Hamming distance of q-ary quantum code than some previous results.

关键词： Norm-trace curve Algebraic geometry code One-point code Dual code quantum code

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quantum codes from trace codes

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2023年第2期69卷 1583-1598页

作者： Kumar, Pavan Khan, Noor Mohammad Aligarh Muslim Univ Dept Math Aligarh 202002 Uttar Pradesh India

For an odd prime p and a positive integer m, let F-pm be the finite field with p(m) elements. For D-1 = {d is an element of F*(pm) : Tr-e(m) (d(2)) = 0) = {d(1), d(2), ..., d(n))(say) and D-2 = {d is an element of F-pm : d(k) = 1} {k = p(l) - 1 for a divisor l of m), first we define classical linear codes by C-D(1) = {(Tr-e(m) (ad(1)), Tr-e(m) (ad(2)), ..., Tr-e(m) (ad(n))) : a is an element of F-pm};(C) over bar (D1) = {(u + Tr-e(m)(ad(1)), u + Tr-e(m) (ad2), ..., u + Tr-e(m) (ad(n))) : a is an element of F-pm, u is an element of F-pe} C-D(2) = {(Tr-e(m) (ad(1)), ..., Tr-e(m)(ad(k)), u + Tr-e(m) (ad(1)), ..., u +Tr-e(m) (ad(k))) : a is an element of F-pm, u is an element of F-pe}, where Tr-e(m) denotes the trace function from F-pm onto F-pe and e is a divisor of m. Then we determine weight distribution of the code (C) over bar (D1) \C-D(1) and construct quantum codes from the codes C-D1 and (C) over bar (D1) based on CSS code construction. Finally, we construct quantum code from the code C-D(2) and show that the code obtained from C-D2 is MDS if and only if s = 1, where s = m/e.

关键词： Linear code Gauss sum Weight distribution quantum code

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