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In this paper, some nonbinary quantum codes using classical codes over Gaussian integers are obtained. Also, some of our quantum codes are better than or comparable with those known before, (for instance [[8; 2; 5]]4+i).

Information Theory · Computer Science 2012-01-16 Murat Güzeltepe , Mehmet Özen

In this paper, we construct self-dual codes from a construction that involves both block circulant matrices and block quadratic residue circulant matrices. We provide conditions when this construction can yield self-dual codes. We construct…

Rings and Algebras · Mathematics 2020-04-02 Joe Gildea , Abidin Kaya , Rhian Taylor , Alexander Tylyshchak , Bahattin Yildiz

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…

We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ with symmetric generator matrices from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$. Using this method, we improve the…

Information Theory · Computer Science 2021-02-22 Whan-Hyuk Choi , Jon-Lark Kim

In this paper, a construction of a pair of "regular" quasi-cyclic LDPC codes as ingredient codes for a quantum error-correcting code is proposed. That is, we find quantum regular LDPC codes with various weight distributions. Furthermore our…

Quantum Physics · Physics 2016-11-18 Manabu Hagiwara , Hideki Imai

We introduce a class of cyclic quantum codes, basing the construction not on the simplicity of the stabilizers, but rather on the simplicity of preparation of a code state (at least in the absence of noise). We show how certain known codes,…

Quantum Physics · Physics 2025-10-21 Matthew B. Hastings

Quantum synchronizable error-correcting codes are special quantum error-correcting codes that are designed to correct both the effect of quantum noise on qubits and misalignment in block synchronization. It is known that in principle such a…

Quantum Physics · Physics 2014-11-17 Yuichiro Fujiwara , Peter Vandendriessche

We characterize the affine-invariant maximal extended cyclic codes. Then by the CSS construction, we derive from these codes a family of pure quantum codes. Also for ordnq even, a new family of degenerate quantum stabilizer codes is derived…

Information Theory · Computer Science 2007-11-14 Kenza Guenda

We consider quantum MDS (QMDS) codes for quantum systems of dimension $q$ with lengths up to $q^2+2$ and minimum distances up to $q+1$. We show how starting from QMDS codes of length $q^2+1$ based on cyclic and constacyclic codes, new QMDS…

Quantum Physics · Physics 2016-01-25 Markus Grassl , Martin Roetteler

Hybrid codes simultaneously encode both quantum and classical information into physical qubits. We give several general results about hybrid codes, most notably that the quantum codes comprising a genuine hybrid code must be impure and that…

Quantum Physics · Physics 2020-09-11 Andrew Nemec , Andreas Klappenecker

In this paper, we present two new ways of quantum synchronization coding based on the $(\bm{u}+\bm{v}|\bm{u}-\bm{v})$ construction and the product construction respectively, and greatly enrich the varieties of available quantum…

Quantum Physics · Physics 2019-07-22 Lan Luo , Zhi Ma , Dongdai Lin

We propose two types, namely Type-I and Type-II, quantum stabilizer codes using quadratic residue sets of prime modulus given by the form $p=4n\pm1$. The proposed Type-I stabilizer codes are of cyclic structure and code length $N=p$. They…

Information Theory · Computer Science 2014-08-01 Yixuan Xie , Jinhong Yuan , Qifu , Sun

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. This paper contributes to constructing two classes…

Information Theory · Computer Science 2021-07-08 Tao Wang , Tongjiang Yan , Vladimir Sidorenko , Xueting Wang

In this paper, necessary and sufficient conditions for the self-orthogonality of t-generator quasi-cyclic (QC) codes are presented under the Euclidean, Hermitian, and symplectic inner products, respectively. Particularly, by studying the…

Information Theory · Computer Science 2025-08-13 Mengying Gao , Yuhua Sun , Tongjiang Yan , Chun'e Zhao

In this article, we construct new non-binary quantum codes from skew constacyclic codes over finite commutative non-chain ring $\mathcal{R}= \mathbb{F}_{p^m}[v]/\langle v^3 =v \rangle$ where $p$ is an odd prime and $m \geq 1$. In order to…

Information Theory · Computer Science 2020-10-15 Ram Krishna Verma , Om Prakash , Ashutosh Singh

In this paper, constructions of some double circulant self-dual codes by generalized cyclotomic classes of order two are presented. This technique is applied to [72, 36, 12] binary highest know self-dual codes to obtain self-dual codes over…

Information Theory · Computer Science 2019-12-16 Wenpeng Gao , Tongjiang Yan

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

In this paper, we mainly consider quasi-cyclic (QC) codes over finite chain rings. We study module structures and trace representations of QC codes, which lead to some lower bounds on the minimum Hamming distance of QC codes. Moreover, we…

Information Theory · Computer Science 2013-09-09 Jian Gao , Linzhi Shen , Fang-Wei Fu

Binary cyclic codes have been a hot topic for many years, and significant progress has been made in the study of this types of codes. As is well known, it is hard to construct infinite families of binary cyclic codes [n, n+1/2] with good…

Information Theory · Computer Science 2024-04-30 Tingting Wu , Lanqiang Li , Xiuyu Zhang , Shixin Zhu

Construction of good quantum codes via classical codes is an important task for quantum information and quantum computing. In this work, by virtue of a decomposition of the defining set of constacyclic codes we have constructed eight new…

Information Theory · Computer Science 2019-01-11 Mehmet E. Koroglu