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Using algebraic geometry codes we give a polynomial construction of quantum codes with asymptotically non-zero rate and relative distance.

Quantum Physics · Physics 2009-11-06 A. Ashikhmin , S. Litsyn , M. A. Tsfasman

Algebraic-geometric codes on Garcia-Stichtenoth family of curves are used to construct the asymptotically good quantum codes.

Quantum Physics · Physics 2007-05-23 Hao Chen

We explicitly construct an infinite family of asymptotically good concatenated quantum stabilizer codes where the outer code uses CSS-type quantum Reed-Solomon code and the inner code uses a set of special quantum codes. In the field of…

Quantum Physics · Physics 2009-01-06 Zhuo Li , Li-Juan Xing , Xin-Mei Wang

In this note, we present a construction of new nonbinary quantum codes with good parameters. These codes are obtained by applying the Calderbank-Shor-Steane (CSS) construction. In order to do this, we show the existence of (classical)…

Quantum Physics · Physics 2017-05-24 Giuliano G. La Guardia

We construct quantum codes that support transversal $CCZ$ gates over qudits of arbitrary prime power dimension $q$ (including $q=2$) such that the code dimension and distance grow linearly in the block length. The only previously known…

Quantum Physics · Physics 2024-08-20 Louis Golowich , Venkatesan Guruswami

We present several results on quantum codes over general alphabets (that is, in which the fundamental units may have more than 2 states). In particular, we consider codes derived from finite symplectic geometry assumed to have additional…

Quantum Physics · Physics 2007-05-23 Eric M. Rains

In this paper, we construct new sequences of asymptotically good convolutional codes. These sequences are obtained from sequences of transitive, self-orthogonal and self-dual block codes that attain the Tsfasman-Vladut-Zink bound.…

Combinatorics · Mathematics 2018-03-29 Giuliano Gadioli La Guardia

We present new quantum codes with good parameters which are constructed from self-orthogonal algebraic geometry codes. Our method permits a wide class of curves to be used in the formation of these codes, which greatly extends the class of…

Algebraic Geometry · Mathematics 2025-01-17 Fernando Hernando , Gary McGuire , Francisco Monserrat , Julio José Moyano-Fernández

In this paper, based on the nonbinary graph state, we present a systematic way of constructing good non-binary quantum codes, both additive and nonadditive, for systems with integer dimensions. With the help of computer search, which…

Quantum Physics · Physics 2009-11-13 Dan Hu , Weidong Tang , Meisheng Zhao , Qing Chen , Sixia Yu , C. H. Oh

If C is a binary linear code, let C^2 be the linear code spanned by intersections of pairs of codewords of C. We construct an asymptotically good family of binary linear codes such that, for C ranging in this family, the C^2 also form an…

Information Theory · Computer Science 2012-09-03 Hugues Randriambololona

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…

Information Theory · Computer Science 2023-01-09 Chaofeng Guan , Ruihu Li , Liangdong Lu , Yu Yao

Quantum error correction is rapidly seeing first experimental implementations, but there is a significant gap between asymptotically optimal error-correcting codes and codes that are experimentally feasible. Quantum LDPC codes range from…

It is reasonable to expect the theory of quantum codes to be simplified in the case of codes of minimum distance 2; thus, it makes sense to examine such codes in the hopes that techniques that prove effective there will generalize. With…

Quantum Physics · Physics 2007-05-23 Eric M. Rains

Using the Calderbank-Shor-Steane (CSS) construction, pure $q$-ary asymmetric quantum error-correcting codes attaining the quantum Singleton bound are constructed. Such codes are called pure CSS asymmetric quantum maximum distance separable…

Information Theory · Computer Science 2016-04-18 Martianus Frederic Ezerman , Somphong Jitman , Han Mao Kiah , San Ling

It is an important task to construct quantum maximum-distance-separable (MDS) codes with good parameters. In the present paper, we provide six new classes of q-ary quantum MDS codes by using generalized Reed-Solomon (GRS) codes and…

Information Theory · Computer Science 2019-12-06 Weijun Fang , Fang-Wei Fu

In this paper, we utilize a concatenation scheme to construct new families of quantum error correction codes achieving the quantum Gilbert-Varshamov (GV) bound asymptotically. We concatenate alternant codes with any linear code achieving…

Quantum Physics · Physics 2023-01-12 Jihao Fan , Jun Li , Ya Wang , Yonghui Li , Min-Hsiu Hsieh , Jiangfeng Du

In this paper, we provide two methods of constructing quantum codes from linear codes over finite chain rings. The first one is derived from the Calderbank-Shor-Steane (CSS) construction applied to self-dual codes over finite chain rings.…

Information Theory · Computer Science 2017-04-24 Xiusheng Liu , Hualu Liu

Good quantum codes, such as quantum MDS codes, are typically nondegenerate, meaning that errors of small weight require active error-correction, which is--paradoxically--itself prone to errors. Decoherence free subspaces, on the other hand,…

Quantum Physics · Physics 2007-05-23 Salah A. Aly , Andreas Klappenecker , Pradeep Kiran Sarvepalli

A class of powerful $q$-ary linear polynomial codes originally proposed by Xing and Ling is deployed to construct good asymmetric quantum codes via the standard CSS construction. Our quantum codes are $q$-ary block codes that encode $k$…

Information Theory · Computer Science 2016-04-18 Martianus Frederic Ezerman , Somphong Jitman , Patrick Solé

In this paper, we propose a sufficient condition for a family of 2-generator self-orthogonal quasi-cyclic codes with respect to Hermitian inner product. Supported in the Hermitian construction, we show algebraic constructions of good…

Information Theory · Computer Science 2025-11-25 Liangdong Lu , Gaochi Zhang , Ganyu Feng , Wenzheng Ma
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