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We investigate CSS and CSS-T quantum error-correcting codes from the point of view of their existence, rarity, and performance. We give a lower bound on the number of pairs of linear codes that give rise to a CSS code with good correction…

Information Theory · Computer Science 2024-05-29 Elena Berardini , Alessio Caminata , Alberto Ravagnani

In this paper, we define and study \emph{quantum cyclic codes}, a generalisation of cyclic codes to the quantum setting. Previously studied examples of quantum cyclic codes were all quantum codes obtained from classical cyclic codes via the…

Information Theory · Computer Science 2010-07-13 Sagarmoy Dutta , Piyush P Kurur

Given a Calderbank-Shor-Steane (CSS) code, it is sometimes necessary to modify the code by adding an arbitrary number of physical qubits and parity checks. Motivations may include concatenating codes, embedding low-density parity check…

Quantum Physics · Physics 2026-03-06 Andrew C. Yuan

We consider design of the quantum stabilizer codes via a two-step, low-complexity approach based on the framework of codeword-stabilized (CWS) codes. In this framework, each quantum CWS code can be specified by a graph and a binary code.…

Quantum Physics · Physics 2012-02-23 Alexey A. Kovalev , Ilya Dumer , Leonid P. Pryadko

We present a family of quantum stabilizer codes using the structure of duadic constacyclic codes over $\mathbb{F}_4$. Within this family, quantum codes can possess varying dimensions, and their minimum distances are lower bounded by a…

Information Theory · Computer Science 2024-05-28 Reza Dastbasteh , Josu Etxezarreta Martinez , Andrew Nemec , Antonio deMarti iOlius , Pedro Crespo Bofill

A conjugate code pair is defined as a pair of linear codes either of which contains the dual of the other. A conjugate code pair represents the essential structure of the corresponding Calderbank-Shor-Steane (CSS) quantum error-correcting…

Information Theory · Computer Science 2007-07-13 Mitsuru Hamada

We present new constructions of binary quantum codes from quaternary linear Hermitian self-dual codes. Our main ingredients for these constructions are nearly self-orthogonal cyclic or duadic codes over F_4. An infinite family of…

Information Theory · Computer Science 2022-11-03 Reza Dastbasteh , Petr Lisonek

Sarvepalli and Klappenecker showed how classical one-point codes on the Hermitian curve can be used to construct quantum codes. Homma and Kim determined the parameters of a larger family of codes, the two-point codes. In quantum…

Information Theory · Computer Science 2011-02-18 Martianu Frederic Ezerman , Radoslav Kirov

New infinite families of quantum symmetric and asymmetric codes are constructed. Several of these are MDS. The codes obtained are shown to have parameters which are better than previously known. A number of known codes are special cases of…

Information Theory · Computer Science 2012-08-14 Kenza Guenda , T. Aaron Gulliver

In this work, our main objective is to construct quantum codes from quasi-twisted (QT) codes. At first, a necessary and sufficient condition for Hermitian self-orthogonality of QT codes is introduced by virtue of the Chinese Remainder…

Information Theory · Computer Science 2020-01-07 Jingjie Lv , Ruihu Li , Junli Wang

We discuss quantum two-block codes, a large class of CSS codes constructed from two commuting square matrices.Interesting families of such codes are generalized-bicycle (GB) codes and two-block group-algebra (2BGA) codes, where a cyclic…

Quantum Physics · Physics 2023-08-01 Renyu Wang , Hsiang-Ku Lin , Leonid P. Pryadko

We show how good quantum error-correcting codes can be constructed using generalized concatenation. The inner codes are quantum codes, the outer codes can be linear or nonlinear classical codes. Many new good codes are found, including both…

Quantum Physics · Physics 2010-06-01 Markus Grassl , Peter W. Shor , Bei Zeng

In this paper we investigate the class of constacyclic codes, which is a natural generalization of the class of cyclic and negacyclic codes. This class of codes is interesting in the sense that it contains codes with good or even optimal…

Information Theory · Computer Science 2016-02-12 Giuliano G. La Guardia

As a generalization of cyclic codes, quasi-cyclic (QC) codes contain many good linear codes. But quasi-cyclic codes studied so far are mainly limited to one generator (1-generator) QC codes. In this correspondence, 2-generator and…

Information Theory · Computer Science 2007-07-16 Eric Zhi Chen

One of the central tasks in quantum error-correction is to construct quantum codes that have good parameters. In this paper, we construct three new classes of quantum MDS codes from classical Hermitian self-orthogonal generalized…

Information Theory · Computer Science 2015-08-06 Tao Zhang , Gennian Ge

Quantum synchronizable codes (QSCs) are special quantum error-correcting codes which can be used to correct the effects of quantum noise on qubits and misalignment in block synchronization. In this paper, a new class of quantum…

Quantum Physics · Physics 2021-10-27 Shiwen Sun , Tongjiang Yan , Yuhua Sun , Tao Wang , Xueting Wang

It is recently conjectured in quantum information processing that phase-shift errors occur with high probability than qubit-flip errors, hence the former is more disturbing to quantum information than the later one. This leads us to…

Information Theory · Computer Science 2009-11-30 Salah A. Aly

Construction of quantum codes and entanglement-assisted quantum codes with good parameters via classical codes is an important task for quantum computing and quantum information. In this paper, by a family of one-generator quasi-cyclic…

Information Theory · Computer Science 2020-09-08 Jingjie Lv , Ruihu Li , Yu Yao

Quantum synchronizable codes are kinds of quantum error-correcting codes that can not only correct the effects of quantum noise on qubits but also the misalignment in block synchronization. In this paper, the quantum synchronizable codes…

Cryptography and Security · Computer Science 2021-05-11 Tao Wang , Tongjiang Yan , Xueting Wang

Quantum maximal-distance-separable (MDS) codes form an important class of quantum codes. It is very hard to construct quantum MDS codes with relatively large minimum distance. In this paper, based on classical constacyclic codes, we…

Information Theory · Computer Science 2014-05-22 Liqi Wang , Shixin Zhu