arXiv:1308.3577 · IEEE International Symposium on Information Theory (ISIT)

A construction of quantum codes via a class of classical polynomial codes

Lingfei Jin, Chaoping Xing

Published Jul 1, 2012• 2 citations

Abstract

There have been various constructions of classical codes from polynomial valuations in literature [2], [7], [8], [10], [11]. In this paper, we present a construction of classical codes based on polynomial construction again. One of the features of this construction is that not only the classical codes arisen from the construction have good parameters, but also quantum codes with reasonably good parameters can be produced from these classical codes. In particular, some new quantum codes are constructed (see Examples V.5 and V.6).

DOI: 10.1109/isit.2012.6284204

Related papers

Quantum Codes Derived From Certain Classes of Polynomials

Tao Zhang, Gennian Ge

One central theme in quantum error-correction is to construct quantum codes that have a relatively large minimum distance. In this paper, we first present a construction of classical linear codes based on certain classes of polynomials. Through these classical linear codes, we are able to obtain some new quantum codes. It turns out that some of the quantum codes exhibited here have better parameters than the ones available in the literature.

IEEE Transactions on Information TheorySep 21, 201614 citations

Quantum Block and Synchronizable Codes Derived from Certain Classes of Polynomials

Tao Zhang, Gennian Ge

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 codes, we are able to obtain some new quantum codes. It turns out that some of quantum codes exhibited here have better parameters than the ones available in the literature. Meanwhile, we give a new class of quantum synchronizable codes with highest possible tolerance against misalignment from duadic codes.

arXiv:1508.00974Aug 5, 20152 citations

Quantum Codes from Generalized Reed-Solomon Codes and Matrix-Product Codes

Tao Zhang, Gennian Ge

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 Reed-Solomon codes. We also present some classes of quantum codes from matrix-product codes. It turns out that many of our quantum codes are new in the sense that the parameters of quantum codes cannot be obtained from all previous constructions.

arXiv:1508.00978Aug 5, 20157 citations

Some classes of concatenated quantum codes: constructions and lower bounds

Hachiro Fujita

In classical coding theory code concatenation is successfully used to construct good errorcorrecting codes and most of the asymptotically good codes known so far are based on concatenation. In this paper we present some classes of asymptotically good concatenated quantum codes, which are a quantum analogue of classical concatenated codes, and derive lower bounds on the minimum distance and the rate of the codes. Our bounds improve on the best lower bound of Ashikhmin–Litsyn–Tsfasman and Matsumoto for rates smaller than about one half. We also give a polynomial-time decoding algorithm for the codes that can decode up to one fourth of the lower bound on the minimum distance of the codes.

Quantum Information and ComputationApr 1, 20151 citation

A New Description of the Additive Quantum Codes

Liu Huan-ping

A new description of the additive quantum codes is presented and a new way to construct good quantum codes [[n,k,d]] is given by using classical binary codes with specific properties in F23n. We show several consequences and examples of good quantum codes by using our new description of the additive quantum codes.

东北数学：英文版Jan 1, 20060 citations

Classical self-orthogonal codes and their applications to quantum codes

Lingfei Jin

After the pioneering work of Shor and Steane, we are able to establish links between quantum codes and classical codes with certain self-orthogonality. Therefore, constructing classical self-orthogonal codes with small dimension and large dual distance becomes our centre point due to the interesting application to quantum codes. \n \n \n \nOne of the most interesting and useful families of classical codes are MDS codes. We will show a systematic construction for classical Hermitian self-orthogonal MDS codes through generalized Reed-Solomn codes. Afterwards, new families of quantum MDS codes can be produced. \n \n \n \nClassical BCH codes would be another good choice for self-orthogonal codes. We show the dual containment through polynomial evaluations, simply by choosing suitable cyclotomic cosets. As a result, quantum codes with good parameters can be derived. \n \n \n \nAnother good candidate of classical codes to investigate for dual containment comes from the class of \n \nalgebraic geometry codes. Instead of testing for dual containment directly, this thesis explores an equivalent condition for the existence of self-orthogonal AG codes. \n \n \n \nAfter various constructions for quantum codes, this thesis ends with a study on bounds for estimating the parameters of codes.

Jan 1, 20130 citations