Constructions of new families of nonbinary quantum codes

被引：91

作者：

La Guardia, Giuliano G. ^{[1
]}

机构：

[1] State Univ Ponta Grossa UEPG, Dept Math & Stat, BR-84030900 Ponta Grossa, PR, Brazil

来源：

PHYSICAL REVIEW A | 2009年 / 80卷 / 04期

关键词：

error correction codes; quantum theory; ERROR-CORRECTING CODES; BINARY CONSTRUCTION;

D O I：

10.1103/PhysRevA.80.042331

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

Three code constructions generating new families of good nonbinary quantum codes are presented in this paper. The first two ones are derived from Hermitian self-orthogonal non-narrow-sense Bose-Chaudhuri-Hocquenghem (BCH) codes. The third one is derived from q-ary (q not equal 2 is a prime power) Steane's enlargement of Calderbank-Shor-Steane codes applied to Euclidean self-orthogonal non-narrow-sense BCH codes. The quantum nonbinary BCH codes presented here have parameters better than the ones available in the literature.

引用

页数：11

共 47 条

[21]

Grassl M, 1999, LECT NOTES COMPUT SC, V1719, P231

[22] On optimal quantum codes [J].

Grassl, M ;

Beth, T ;

Rötteler, M .

INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, 2004, 2 (01) :55-64

[23] Codes for the quantum erasure channel [J].

Grassl, M ;

Beth, T ;

Pellizzari, T .

PHYSICAL REVIEW A, 1997, 56 (01) :33-38

[24]

Grassl M., 1999, PROC X INT S THEORET, P207

[25] Generalized concatenated quantum codes [J].

Grassl, Markus ;

Shor, Peter ;

Smith, Graeme ;

Smolin, John ;

Zeng, Bei .

PHYSICAL REVIEW A, 2009, 79 (05)

[26] QUANTUM DUADIC AND AFFINE-INVARIANT CODES [J].

Guenda, Kenza .

INTERNATIONAL JOURNAL OF QUANTUM INFORMATION, 2009, 7 (01) :373-384

[27] Concatenated Quantum Codes Constructible in Polynomial Time: Efficient Decoding and Error Correction [J].

Hamada, Mitsuru .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2008, 54 (12) :5689-5704

[28]

Hocquenghem A., 1959, CHIFFRES, V2, P147

[29] Nonbinary stabilizer codes over finite fields [J].

Ketkar, Avanti ;

Klappenecker, Andreas ;

Kumar, Santosh ;

Sarvepalli, Pradeep Kiran .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2006, 52 (11) :4892-4914

[30] Fault-tolerant quantum computation by anyons [J].

Kitaev, AY .

ANNALS OF PHYSICS, 2003, 303 (01) :2-30

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