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Quantum maximum-distance-separable (MDS for short) codes are an important class of quantum codes. In this paper, by using Hermitian self-orthogonal generalized Reed-Solomon (GRS for short) codes, we construct five new classes of $q$-ary…

Information Theory · Computer Science 2023-07-11 Ruhao Wan , Shixin Zhu

In this paper, we construct the first families of asymmetric quantum convolutional codes (AQCC)'s. These new AQCC's are constructed by means of the CSS-type construction applied to suitable families of classical convolutional codes, which…

Quantum Physics · Physics 2016-10-05 Giuliano G. La Guardia

We investigate CSS and CSS-T quantum error-correcting codes from the point of view of their existence, rarity, and performance. We give a lower bound on the number of pairs of linear codes that give rise to a CSS code with good correction…

Information Theory · Computer Science 2024-05-29 Elena Berardini , Alessio Caminata , Alberto Ravagnani

We give a construction of Quantum Low-Density Parity Check (QLDPC) codes with near-optimal rate-distance tradeoff and efficient list decoding up to the Johnson bound in polynomial time. Previous constructions of list decodable good distance…

Information Theory · Computer Science 2024-11-08 Thiago Bergamaschi , Fernando Granha Jeronimo , Tushant Mittal , Shashank Srivastava , Madhur Tulsiani

In this paper a construction of quantum codes from self-orthogonal algebraic geometry codes is provided. Our method is based on the CSS construction as well as on some peculiar properties of the underlying algebraic curves, named Swiss…

Algebraic Geometry · Mathematics 2019-12-18 Daniele Bartoli , Maria Montanucci , Giovanni Zini

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…

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

There has been a lot of effort to construct good quantum codes from the classical error correcting codes. Constructing new quantum codes, using Hermitian self-orthogonal codes, seems to be a difficult problem in general. In this paper,…

Information Theory · Computer Science 2021-12-14 Lin Sok

This paper is motivated by the computer-generated nonadditive ((5,6,2)) code described in an article by Rains, Hardin, Shor and Sloane. We describe a theory of non-stabilizer codes of which the nonadditive code of Rains et al is an example.…

Quantum Physics · Physics 2007-05-23 V. Arvind , Piyush P Kurur , K. R. Parthasarathy

Four quantum code constructions generating several new families of good nonbinary quantum nonprimitive non-narrow-sense Bose-Chaudhuri-Hocquenghem (BCH) codes are presented in this paper. The first two ones are based on…

Quantum Physics · Physics 2016-11-17 Giuliano G. La Guardia

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…

Information Theory · Computer Science 2014-04-01 Liqi Wang , Shixin Zhu

We construct families of high performance quantum amplitude damping codes. All of our codes are nonadditive and most modestly outperform the best possible additive codes in terms of encoded dimension. One family is built from nonlinear…

Quantum Physics · Physics 2009-07-30 Peter W. Shor , Graeme Smith , John A. Smolin , Bei Zeng

We present new constructions of binary quantum codes from quaternary linear Hermitian self-dual codes. Our main ingredients for these constructions are nearly self-orthogonal cyclic or duadic codes over F_4. An infinite family of…

Information Theory · Computer Science 2022-11-03 Reza Dastbasteh , Petr Lisonek

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

We describe a general method for turning quantum circuits into sparse quantum subsystem codes. The idea is to turn each circuit element into a set of low-weight gauge generators that enforce the input-output relations of that circuit…

Quantum Physics · Physics 2017-03-28 Dave Bacon , Steven T. Flammia , Aram W. Harrow , Jonathan Shi

We present families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal. These maximum distance separable (MDS) codes are defined over q-dimensional quantum systems, where q is an arbitrary…

Quantum Physics · Physics 2023-11-27 Markus Grassl , Thomas Beth , Martin Roetteler

We study Algebraic Geometry codes producing quantum error-correcting codes by the CSS construction. We pay particular attention to the family of Castle codes. We show that many of the examples known in the literature in fact belong to this…

Information Theory · Computer Science 2016-06-30 Carlos Munuera , Wanderson Tenório , Fernando Torres

Most known quantum codes are additive, meaning the codespace can be described as the simultaneous eigenspace of an abelian subgroup of the Pauli group. While in some scenarios such codes are strictly suboptimal, very little is understood…

Quantum Physics · Physics 2009-11-13 John A. Smolin , Graeme Smith , Stephanie Wehner

It is a major challenge to construct good quantum codes supporting fault-tolerant (e.g. transversal) non-Clifford gates with low-weight parity-check measurements. In this paper, we construct the first known quantum codes with linear…

Quantum Physics · Physics 2025-10-09 Louis Golowich , Venkatesan Guruswami

In this paper, two classes of quantum MDS codes are constructed. The main tools are multiplicative structures on finite fields. Carefully choosing different cosets can make the corresponding generalized Reed-Solomon codes Hermitian…

Information Theory · Computer Science 2024-10-24 Puyin Wang , Jinquan Luo

This work develops a geometric framework for constructing quantum error-correcting codes from weighted projective and orbifold structures, integrating algebraic geometry, divisor theory, and the CSS stabilizer formalism. Beginning with…

Quantum Physics · Physics 2026-02-26 Tony Shaska