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Related papers: Asymmetric quantum convolutional codes

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One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. In this paper, we first present a construction of classical codes based on certain class of polynomials. Through these classical…

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

This paper is devoted to the study of the construction of new quantum MDS codes. Based on constacyclic codes over Fq2 , we derive four new families of quantum MDS codes, one of which is an explicit generalization of the construction given…

Information Theory · Computer Science 2017-05-08 Mustafa Sari , Emre Kolotoglu

We present a general construction of asymmetric quantum codes based on additive codes under the trace Hermitian inner product. Various families of additive codes over $\F_{4}$ are used in the construction of many asymmetric quantum codes…

Information Theory · Computer Science 2013-07-04 Martianus Frederic Ezerman , San Ling , Patrick Sole

Quantum synchronizable codes are quantum error-correcting codes designed to correct the effects of both quantum noise and block synchronization errors. While it is known that quantum synchronizable codes can be constructed from cyclic codes…

Information Theory · Computer Science 2014-08-19 Yixuan Xie , Jinhong Yuan , Yuichiro Fujiwara

Recently, the theory of quantum error control codes has been extended to subsystem codes over symmetric and asymmetric quantum channels -- qubit-flip and phase-shift errors may have equal or different probabilities. Previous work in…

Quantum Physics · Physics 2008-11-11 Salah A. Aly

We give an asymptotically good family of quantum CSS codes on qubits with a transversal CCZ gate, meaning that the parallel logical CCZ on all logical qubits is performed by parallel physical CCZs on (a subset of) physical qubits. The…

Quantum Physics · Physics 2024-10-15 Quynh T. Nguyen

The theory of entanglement-assisted quantum error-correcting codes (EAQECCs) is a generalization of the standard stabilizer quantum error-correcting codes, which can be possibly constructed from any classical codes by relaxing the duality…

Information Theory · Computer Science 2023-05-16 Xiaojing Chen , Xingbo Lu , Shixin Zhu , Wan Jiang , Xindi Wang

We present a new propagation rule for CSS codes. Starting with a CSS code $[\![n,k,d]\!]_q$, we construct a CSS code with parameters $[\![n-2,k,d-1]\!]_q$. In general, one would only obtain a code with parameters $[\![n-2,k,d-2]\!]_q$. The…

Quantum Physics · Physics 2023-10-06 Markus Grassl

Asymmetric quantum error-correcting codes are quantum codes defined over biased quantum channels: qubit-flip and phase-shift errors may have equal or different probabilities. The code construction is the Calderbank-Shor-Steane construction…

Cryptography and Security · Computer Science 2017-08-10 Johan P. Hansen

A class of powerful $q$-ary linear polynomial codes originally proposed by Xing and Ling is deployed to construct good asymmetric quantum codes via the standard CSS construction. Our quantum codes are $q$-ary block codes that encode $k$…

Information Theory · Computer Science 2016-04-18 Martianus Frederic Ezerman , Somphong Jitman , Patrick Solé

There have been various constructions of classical codes from polynomial valuations in literature \cite{ARC04, LNX01,LX04,XF04,XL00}. In this paper, we present a construction of classical codes based on polynomial construction again. One of…

Information Theory · Computer Science 2013-08-19 Lingfei Jin , Chaoping Xing

We present a general framework of quantum error-correcting codes (QECCs) as a subspace of a complex Hilbert space and the corresponding error models. Then we illustrate how QECCs can be constructed using techniques from algebraic coding…

Information Theory · Computer Science 2022-03-08 Markus Grassl

Quasi-cyclic codes have been recently employed in the constructions of quantum error-correcting codes. In this paper, we propose a construction of infinite families of quasi-cyclic codes over $\F_q$ which are self-orthogonal with respect to…

Information Theory · Computer Science 2026-05-25 Gustavo Terra Bastos , Angelynn Álvarez , Cameron Williams

In this study, we investigate the construction of quantum CSS duadic codes with dimensions greater than one. We introduce a method for extending smaller splittings of quantum duadic codes to create larger, potentially degenerate quantum…

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 properties of $q$-ary cyclotomic cosets modulo $n = q^{m} - 1$, where $q \geq 3$ is a prime power, are investigated in this paper. Based on these properties, the dimension as well as bounds for the designed distance of some families of…

Information Theory · Computer Science 2016-01-01 Giuliano Gadioli La Guardia , Marcelo Muniz Silva Alves

In this paper, we introduce a construction of quantum convolutional codes (QCCs) based on difference triangle sets (DTSs). To construct QCCs, one must determine polynomial stabilizers $X(D)$ and $Z(D)$ that commute (symplectic…

Information Theory · Computer Science 2026-02-17 Vahid Nourozi , David Mitchell

We present new quantum codes with good parameters which are constructed from self-orthogonal algebraic geometry codes. Our method permits a wide class of curves to be used in the formation of these codes, which greatly extends the class of…

Algebraic Geometry · Mathematics 2025-01-17 Fernando Hernando , Gary McGuire , Francisco Monserrat , Julio José Moyano-Fernández

Quantum error correcting codes (QECC) is becoming an increasingly important branch of coding theory. For classical block codes, a \href{codetables.de} {comprehensive database of best known codes} exists which is available online at…

Information Theory · Computer Science 2021-08-21 Nuh Aydin , Peihan Liu , Bryan Yoshino

Quantum convolutional codes can be used to protect a sequence of qubits of arbitrary length against decoherence. In this paper, we give two new constructions of quantum MDS convolutional codes derived from generalized Reed-Solomon codes and…

Information Theory · Computer Science 2015-11-06 Baokun Ding , Tao Zhang , Gennian Ge