Liqi Wang

• PhD
• Hefei University of Technology

Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_{q^{2}}\mathcal {R}=\mathbb {F}_{q^{2}} \times (\mathbb {F}_{q^{2}}+v\mathbb {F}_{q^{2}})$$\end{document...

Entanglement-assisted quantum error-correcting codes (EAQECCs) not only can boost the performance of stabilizer quantum error-correcting codes but also can be derived from arbitrary classical linear codes by loosing the self-orthogonal condition and using pre-shared entangled states between the sender and the receiver. It is a challenging work to c...

By generalizing the stabilizer quantum error-correcting codes, entanglement-assisted quantum error-correcting (EAQEC) codes were introduced, which could be derived from any classical linear codes via the relaxation of self-orthogonality conditions with the aid of pre-shared entanglement between the sender and the receiver. In this paper, three clas...

Entanglement-assisted quantum error-correcting codes as a generalization of stabilizer quantum error-correcting (QEC) codes can improve the performance of stabilizer QEC codes and can be constructed from arbitrary classical linear codes by relaxing the dual-containing condition and using pre-shared entanglement states between the sender and the rec...

Let R=Fpm[u]∕〈u3〉 be the finite commutative chain ring with unity, where p is a prime, m is a positive integer and Fpm is a finite field with pm elements. In this study, we investigate σ-constacyclic codes of length ps over R, that is, ideals of the ring R[x]∕〈xps−σ〉, where σ is a nonzero element of the field Fpm. First, we classify all cyclic code...

Entanglement-assisted quantum error-correcting codes (EAQECCs) can be obtained from arbitrary classical linear codes based on the entanglement-assisted stabilizer formalism, which greatly promoted the development of quantum coding theory. In this paper, we construct several families of [Formula: see text]-ary entanglement-assisted quantum maximum-d...

Any permutation polynomial is an n-cycle permutation. When n is a specific small positive integer, one can obtain efficient permutations, such as involutions, triple-cycle permutations and quadruple-cycle permutations. These permutations have important applications in cryptography and coding theory. Inspired by the AGW criterion, we propose criteri...

Constacyclic codes are a subclass of linear codes and have been well studied. Constacyclic BCH codes are a family of constacyclic codes and contain BCH codes as a subclass. Compared with the in-depth study of BCH codes, there are relatively little study on constacyclic BCH codes. The objective of this paper is to determine the dimension and minimum...

Entanglement-assisted quantum error-correcting codes are a generalization of standard stabilizer quantum error-correcting codes, which can be possibly constructed from any classical codes by relaxing the duality condition and utilizing pre-shared entanglement between the sender and the receiver. In this paper, we construct seven new families of ent...

Cyclic codes are an interesting class of linear codes due to their efficient encoding and decoding algorithms. Bose–Chaudhuri–Hocquenghem (BCH) codes which form a significant subclass of cyclic codes are important in both theory and practice since they have good error-correcting capabilities and have been widely used in communication systems, stora...

Being part of distributed storage systems, locally repairable codes (LRCs) have drawn great attention in the past years. Inspired by a recent construction of optimal LRCs-based on cyclic codes, constacyclic LRCs are studied in this letter. Specifically, a family of optimal constacyclic $(r,\delta)_{q}$ -LRCs with unbounded length and minimum dist...

In this paper, we give the structures of all (1+u+v)-constacyclic codes of length 2s over F2+uF2+vF2+uvF2, we also obtain the number of codewords, and the dual of each constacyclic code. Among other results, we study the form of such constacyclic codes that are self-dual and give the number of these codes. We end by giving all self-dual constacycli...

In this paper, we explicitly determine the generator polynomials of all repeated-root constacyclic codes of length nlps over Fq and their dual codes, where l is an odd prime different from p, and n is an odd prime different from both l and p such that n=2h+1 for some prime h or h=1. Moreover, we give all self-dual cyclic codes of length nlps over F...

Symbol-pair codes are proposed to protect against pair errors in symbol-pair read channel. One main task in symbol-pair coding theory is to determine the minimum pair-distance of symbol-pair codes. In this paper, we investigate the symbol-pair distance of cyclic codes of length pe over \(\phantom {\dot {i}\!}\mathbb {F}_{p^{m}}\). The exact symbol-...

For units δ and α in F p m , the structure of (δ + αu 2)-constacyclic codes of length p k over F p m + uF p m + u 2 F p m is studied and self-dual (δ + αu 2)-constacyclic codes are analyzed.

In this paper, we study one-Lee weight and two-Lee weight codes over $\mathbb{Z}_{2}\mathbb{Z}_{2}[u]$, where $u^{2}=0$. Some properties of one-Lee weight $\mathbb{Z}_{2}\mathbb{Z}_{2}[u]$-additive codes are given, and a complete classification of one-Lee weight $\mathbb{Z}_2\mathbb{Z}_2[u]$-additive formally self-dual codes is obtained. The struct...

Symbol-pair codes are proposed to protect against pair errors in symbol-pair read channels. One of the most important task in symbol-pair coding theory is to determine the minimum pair-distance of symbol-pair codes. In this paper, we investigate the symbol-pair distances of cyclic codes of length $p^e$ over $\mathbb{F}_{p^m}$. The exact symbol-pair...

The aim of this paper is to determine the algebraic structures of all λ-constacyclic codes of length 2ps over the finite commutative chain ring Fpm+uFpm, where p is an odd prime and u2=0. For this purpose, the situation of λ is mainly divided into two cases separately. If the unit λ is not a square and λ=α+uβ for nonzero elements α,β of Fpm, it is...

DNA has a complicated structure with an excellent error correcting capability. Recently, some codes with similar properties as DNA are studied. Cyclic codes of even lengths over \({\mathbb {F}}_2+u{\mathbb {F}}_2\) satisfy the reverse constraint and the reverse-complement constraint are studied in this paper. The existence and the structure of such...

One of the most challenges to prove the feasibility of quantum computers is to protect the quantum nature of information. Quantum convolutional codes are aimed at protecting a stream of quantum information in a long distance communication, which are the correct generalization to the quantum domain of their classical analogs. In this paper, we const...

In this paper, we describe the Chinese Remainder Theorem for studying Abelian codes of length \(N\) over the ring \({\mathbb {Z}}_{m}\), where \(m=\prod _{i=1}^{s}p_{i}, \) \(k=\prod _{i=1}^{s}p_{i}^{t_{i}}, \, N=kn, \, p_{i}\) are distinct primes, \(s\) is a positive integer, \(t_{i}\) are positive integers and \(n\) is a positive integer prime to...

For any odd prime p, the structures of all negacyclic codes of length over the finite commutative chain ring are established in term of their polynomial generators. When , each negacyclic code of length is represented as a direct sum of a −α-constacyclic code and an α-constacyclic code of length . In the case , such negacyclic codes are classified...

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 construct two classes of quantum MDS codes with parameters $$[[\lambda(q-1),\lambda(q-1)-2d+2,d]]_q$$ where $2\leq d\...

In this paper, based on the Steane's enlargement construction, three classes of non-binary quantum codes are constructed from classical repeated-root cyclic codes of length 2p(s) over F-q with odd characteristic p. The exact minimum distances of these quantum codes are determined. This construction yields a quantum MDS code with parameters [[2p, 2p...

Constacyclic codes are important classes of linear codes that have been applied to the construction of quantum codes. Six new families of asymmetric quantum codes derived from constacyclic codes are constructed in this paper. Moreover, the constructed asymmetric quantum codes are optimal and different from the codes available in the literature.

A new Gray map is defined from R=F2+uF2+u2F2 + u3F2 to F24 with u4 = 0. It is proved that the Gray image of a linear (1+u+u2+u3)-cyclic code of length n over R is a distance-invariant linear cyclic code of length 4n over F2. Further more, the generator polynomials of the Gray image of this constacyclic code for odd length over R is determined, some...

This paper studies (1 + u)-constacyclic codes over the ring F 2 + uF 2 + vF 2 + uvF 2. It is proved that the image of a (1+u)-constacyclic code of length n over F 2+uF 2+vF 2+uvF 2 under a Gray map is a distance invariant binary quasi-cyclic code of index 2 and length 4n. A set of generators of such constacyclic codes for an arbitrary length is det...

We introduce a Gray map from Fp+vFpFp+vFp to Fp2 and study (1−2v)(1−2v)-constacyclic codes over Fp+vFpFp+vFp, where v2=vv2=v. It is proved that the image of a (1−2v)(1−2v)-constacyclic code of length nn over Fp+vFpFp+vFp under the Gray map is a distance-invariant linear cyclic code of length 2n2n over FpFp. The generators of such constacyclic codes...