arXiv subjects

Ruihu Li

Publications and source records attributed to Ruihu Li.

At least 19 recordsLinked to original sources

arXiv2026

Construction of EAQECCs with imperfect ebits

We generalize the stabilizer formalism for entanglement-assisted quantum error-correcting codes with noisy ebits (EAQECCs-Ne) from the binary case to the general $q$-ary case, where $q$ is a prime power. By leveraging the structure of the generalized Pauli group over $\mathbb{F}_q$ and symplectic geometry over $\mathbb{F}_q^{2n}$, we establish a unified framework for constructing EAQECCs-Ne for qudit systems. Equivalent formulations in terms of symplectic geometry over $\mathbb{F}_q$ and additive codes over $\mathbb{F}_q^{2n}$ are derived. We further construct several families of $q$-ary EAQECCs with noise ebits and analyze their performance compared to optimal stabilizer codes. Our results demonstrate that under certain noise conditions, the proposed EAQECCs-Ne can outperform standard stabilizer codes with equivalent error-correcting capability, offering a promising approach for fault-tolerant quantum computation in high-dimensional quantum systems.

quant-ph↗

arXiv2026

Stabilizer Formalism for EAQECCs with Noise ebits

We introduce a stabilizer formalism for EAQECCs with noise ebits, using special subgroups of product groups of two Pauli groups. This formalism includes the two coding schemes,given by Lai and Brun (C.Y. Lai and T. A. Brun, PHYSICAL REVIEW A 86, 032319 (2012)), for EAQECCs with imperfect ebits as special cases. Then two equivalent formalisms of the formalism are derived in nomenclature of sympletic geometry and additive codes. We apply this theory to construct some EAQECCs with noise ebits, and analyze their performance.

quant-ph↗

arXiv2025

Geometry of the symplectic group and optimal EAQECC codes

A new type of link between geometry of symplectic group and entanglement-assisted (EA) quantum error-correcting codes (EAQECCs) is presented. Relations of symplectic subspaces and quaternary additive codes concerning parameters of EAQECCs are described. Thus, parameters of EA stabilizer codes are revealed in the nomenclature of additive codes. Our techniques enable us solve some open problems about optimal EAQECCs and entanglement-assisted quantum minimum distance separable (EAQMDS) codes, and are also useful for designing encoding and decoding quantum circuit of EA stabilizer codes.

quant-ph↗

arXiv2024

On the largest minimum distances of [n,6] LCD codes

Linear complementary dual (LCD) codes can be used to against side-channel attacks and fault noninvasive attacks. Let $d_{a}(n,6)$ and $d_{l}(n,6)$ be the minimum weights of all binary optimal linear codes and LCD codes with length $n$ and dimension 6, respectively.In this article, we aim to obtain the values of $d_{l}(n,6)$ for $n\geq 51$ by investigating the nonexistence and constructions of LCD codes with given parameters. Suppose that $s \ge 0$ and $0\leq t\leq 62$ are two integers and $n=63s+t$. Using the theories of defining vectors, generalized anti-codes, reduced codes and nested codes, we exactly determine $d_{l}(n,6)$ for $t \notin\{21,22,25,26,33,34,37,38,45,46\}$, while we show that $d_{l}(n,6)\in$$\{d_{a}(n,6)$ $-1,d_{a}(n,6)\}$ for $t\in\{21,22,26,34,37,38,46\}$ and $ d_{l}(n,6)\in$$ \{d_{a}(n,6)-2,$ $d_{a}(n,6)-1\}$ for$t\in{25,33,45\}$.

cs.IT↗

arXiv2023

Some quaternary additive codes outperform linear counterparts

The additive codes may have better parameters than linear codes. However, it is still a challenging problem to efficiently construct additive codes that outperform linear codes, especially those with greater distances than linear codes of the same lengths and dimensions. This paper focuses on constructing additive codes that outperform linear codes based on quasi-cyclic codes and combinatorial methods. Firstly, we propose a lower bound on the symplectic distance of 1-generator quasi-cyclic codes of index even. Secondly, we get many binary quasi-cyclic codes with large symplectic distances utilizing computer-supported combination and search methods, all of which correspond to good quaternary additive codes. Notably, some additive codes have greater distances than best-known quaternary linear codes in Grassl's code table (bounds on the minimum distance of quaternary linear codes http://www.codetables.de) for the same lengths and dimensions. Moreover, employing a combinatorial approach, we partially determine the parameters of optimal quaternary additive 3.5-dimensional codes with lengths from $28$ to $254$. Finally, as an extension, we also construct some good additive complementary dual codes with larger distances than the best-known quaternary linear complementary dual codes in the literature.

cs.IT↗

arXiv2023

On Euclidean, Hermitian and symplectic quasi-cyclic complementary dual codes

Linear complementary dual codes (LCD) intersect trivially with their dual. In this paper, we develop a new characterization for LCD codes, which allows us to judge the complementary duality of linear codes from the codeword level. Further, we determine the sufficient and necessary conditions for one-generator quasi-cyclic codes to be LCD codes involving Euclidean, Hermitian, and symplectic inner products. Finally, we constructed many Euclidean, Hermitian and symmetric LCD codes with excellent parameters, some improving the results in the literature. Remarkably, we construct a symplectic LCD $[28,6]_2$ code with symplectic distance $10$, which corresponds to an trace Hermitian additive complementary dual $(14,3,10)_4$ code that outperforms the optimal quaternary Hermitian LCD $[14,3,9]_4$ code.

cs.IT↗

arXiv2022

Symplectic self-orthogonal quasi-cyclic codes

In this paper, we establish the necessary and sufficient conditions for quasi-cyclic (QC) codes with index even to be symplectic self-orthogonal. Subsequently, we present the lower and upper bounds on the minimum symplectic distances of a class of $1$-generator QC codes and their symplectic dual codes by decomposing code spaces. As an application, we construct numerous new binary symplectic self-orthogonal QC codes with excellent parameters, leading to $117$ record-breaking quantum error-correction codes.

cs.IT↗

arXiv2022

On construction of quantum codes with dual-containing quasi-cyclic codes

One of the main objectives of quantum error-correction theory is to construct quantum codes with optimal parameters and properties. In this paper, we propose a class of 2-generator quasi-cyclic codes and study their applications in the construction of quantum codes over small fields. Firstly, some sufficient conditions for these 2-generator quasi-cyclic codes to be dual-containing concerning Hermitian inner product are determined. Then, we utilize these Hermitian dual-containing quasi-cyclic codes to produce quantum codes via the famous Hermitian construction. Moreover, we present a lower bound on the minimum distance of these quasi-cyclic codes, which is helpful to construct quantum codes with larger lengths and dimensions. As the computational results, many new quantum codes that exceed the quantum Gilbert-Varshamov bound are constructed over $F_q$, where $q$ is $2,3,4,5$. In particular, 16 binary quantum codes raise the lower bound on the minimum distance in Grassl's table \cite{Grassl:codetables}. In nonbinary cases, many quantum codes are new or have better parameters than those in the literature.

cs.IT↗

arXiv2022

Minimum distances of binary optimal LCD codes of dimension five are completely determined

Let $t \in \{2,8,10,12,14,16,18\}$ and $n=31s+t\geq 14$, $d_{a}(n,5)$ and $d_{l}(n,5)$ be distances of binary $[n,5]$ optimal linear codes and optimal linear complementary dual (LCD) codes, respectively. We show that an $[n,5,d_{a}(n,5)]$ optimal linear code is not an LCD code, there is an $[n,5,d_{l}(n,5)]=[n,5,d_{a}(n,5)-1]$ optimal LCD code if $t\neq 16$, and an optimal $[n,5,d_{l}(n,5)]$ optimal LCD code has $d_{l}(n,5)=16s+6=d_{a}(n,5)-2$ for $t=16$. Combined with known results on optimal LCD code, $d_{l}(n,5)$ of all $[n,5]$ LCD codes are completely determined.

cs.IT↗

arXiv2022

Duality of generalized twisted Reed-Solomon codes and Hermitian self-dual MDS or NMDS codes

Self-dual MDS and NMDS codes over finite fields are linear codes with significant combinatorial and cryptographic applications. In this paper, firstly, we investigate the duality properties of generalized twisted Reed-Solomon (abbreviated GTRS) codes in some special cases. In what follows, a new systematic approach is proposed to draw Hermitian self-dual (+)-GTRS codes. The necessary and sufficient conditions of a Hermitian self-dual (+)-GTRS code are presented.With this method, several classes of Hermitian self-dual MDS and NMDS codes are constructed.

cs.IT↗

arXiv2021

New Binary Quantum Codes Constructed from Quasi-Cyclic Codes

It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of two-generator quasi-cyclic codes and derives sufficient conditions for these codes to be symplectic dual-containing. Then, a new method for constructing binary quantum codes using symplectic dual-containing codes is proposed. As an application, we construct 8 binary quantum codes that exceed the best-known results. Further, another 36 new binary quantum codes are obtained by propagation rules, all of which improve the lower bound on the minimum distances.

cs.IT↗

arXiv2020

Optimal Ternary Linear Complementary Dual Codes

Linear complementary dual (LCD) codes introduced by Massey are the codes whose intersections with their dual codes are trivial. It can help to improve the security of the information processed by sensitive devices, especially against side-channel attacks (SCA) and fault invasive attacks. In this paper, By construction of puncturing, extending, shortening and combination codes, many good ternary LCD codes are presented. We give a Table 1 with the values of $d_{LCD}(n,k)$ for length $ n \leq 20$. In addition, Many of these ternary LCD codes given in this paper are optimal which are saturating the lower or upper bound of Grassl's codetable in \cite{Grassl} and some of them are nearly optimal.

cs.IT↗

arXiv2020

Two families of Entanglement-assisted Quantum MDS Codes from cyclic Codes

With entanglement-assisted (EA) formalism, arbitrary classical linear codes are allowed to transform into EAQECCs by using pre-shared entanglement between the sender and the receiver. In this paper, based on classical cyclic MDS codes by exploiting pre-shared maximally entangled states, we construct two families of $q$-ary entanglement-assisted quantum MDS codes $[[\frac{q^{2}+1}{a},\frac{q^{2}+1}{a}-2(d-1)+c,d;c]]$, where q is a prime power in the form of $am+l$, and $a=(l^2+1)$ or $a=\frac{(l^2+1)}{5}$. We show that all of $q$-ary EAQMDS have minimum distance upper limit much larger than the known quantum MDS (QMDS) codes of the same length. Most of these $q$-ary EAQMDS codes are new in the sense that their parameters are not covered by the codes available in the literature.

cs.IT↗

arXiv2020

Extended quasi-cyclic constructions of quantum codes and entanglement-assisted quantum codes

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 codes, we provide quasi-cyclic extended constructions that preserve the self-orthogonality to obtain stabilizer quantum codes. As for the computational results, some binary and ternary stabilizer codes with good parameters are constructed. Moreover, we present methods to construct maximal-entanglement entanglement-assisted quantum codes by means of the class of quasi-cyclic codes and their extended codes. As an application, some good maximal-entanglement entanglement-assisted quantum codes are obtained and their parameters are compared.

cs.IT↗

arXiv2020

Additive Conjucyclic Codes over $\F_{q^2}$: Trace Correspondence and Applications to Quantum Codes

Additive conjucyclic codes over $\F_{q^2}$ are closed under the conjugated cyclic shift and play an important role in constructing quantum error-correcting codes (QECCs). However, a systematic algebraic theory for such codes over general finite fields has been lacking. In this paper, we develop a unified framework by establishing a trace-based $\F_q$-linear isomorphism between $\F_{q^2}^n$ and $\F_q^{2n}$. This correspondence shows that additive conjucyclic codes of length $n$ correspond bijectively to $q$-ary linear cyclic codes of length $2n$, translating their structural analysis to the well-understood setting of cyclic codes. Using this isomorphism, we determine the enumeration of such codes and give explicit forms of their generator matrices. We then introduce an alternating inner product on $\F_{q^2}^n$, which is shown to be compatible with the symplectic inner product on $\F_q^{2n}$ under the trace isomorphism. Based on this inner product, we characterize the dual-containing condition for additive conjucyclic codes and derive explicit parity-check matrices. Finally, we construct $q$-ary QECCs from dual-containing additive conjucyclic codes. Our results unify and generalize previous studies on quaternary additive conjucyclic codes and present a construction method for $q$-ary QECCs from additive conjucyclic codes, together with an illustrative example.

cs.IT↗

arXiv2019

Constructions of quasi-twisted quantum codes

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 Theorem (CRT). Then we utilize these self-orthogonal QT codes to provide quantum codes via the famous Hermitian Construction. Moreover, we present a new construction method of q-ary quantum codes, which can be viewed as an effective generalization of the Hermitian Construction. General QT codes that are not self-orthogonal are also employed to construct quantum codes. As the computational results, some binary, ternary and quaternary quantum codes are constructed and their parameters are determined, which all exceed the Quantum Gilbert-Varshamov (GV) Bound. In the binary case, a small number of quantum codes are derived with strictly improved parameters compared with the current records. In the ternary and quaternary cases, our codes fill some gaps or have better performances than the current results.

cs.IT↗

arXiv2018

New Quantum MDS codes constructed from Constacyclic codes

Quantum maximum-distance-separable (MDS) codes are an important class of quantum codes. In this paper, using constacyclic codes and Hermitain construction, we construct some new quantum MDS codes of the form $q=2am+t$, $n=\frac{q^{2}+1}{a}$. Most of these quantum MDS codes are new in the sense that their parameters are not covered be the codes available in the literature.

cs.IT↗

arXiv2018

Entanglement-assisted quantum MDS codes from constacyclic codes with large minimum distance

The entanglement-assisted (EA) formalism allows arbitrary classical linear codes to transform into entanglement-assisted quantum error correcting codes (EAQECCs) by using pre-shared entanglement between the sender and the receiver. In this work, we propose a decomposition of the defining set of constacyclic codes. Using this method, we construct four classes of $q$-ary entanglement-assisted quantum MDS (EAQMDS) codes based on classical constacyclic MDS codes by exploiting less pre-shared maximally entangled states. We show that a class of $q$-ary EAQMDS have minimum distance upper limit greater than $3q-1$. Some of them have much larger minimum distance than the known quantum MDS (QMDS) codes of the same length. Most of these $q$-ary EAQMDS codes are new in the sense that their parameters are not covered by the codes available in the literature.

cs.IT↗