On the distance of stabilizer quantum codes from J-affine variety codes

被引：15

作者：

Galindo, Carlos ^{[1
,2
]}

Geil, Olav ^{[3
]}

Hernando, Fernando ^{[1
,2
]}

Ruano, Diego ^{[3
]}

机构：

[1] Univ Jaume 1, Inst Univ Matemat & Aplicac Castellon, Campus Riu Sec, Castellon de La Plana 12071, Spain

[2] Univ Jaume 1, Dept Matemat, Campus Riu Sec, Castellon de La Plana 12071, Spain

[3] Aalborg Univ, Dept Math Sci, Fredrik Bajers Vej 7G, DK-9220 Aalborg, Denmark

来源：

QUANTUM INFORMATION PROCESSING | 2017年 / 16卷 / 04期

关键词：

Stabilizer J-affine variety codes; Subfield-subcodes; Designed minimum distance; Hermitian and Euclidean duality; ERROR-CORRECTING CODES; MDS CODES;

D O I：

10.1007/s11128-017-1559-1

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Self-orthogonal J-affine variety codes have been successfully used to obtain quantum stabilizer codes with excellent parameters. In a previous paper we gave formulae for the dimension of this family of quantum codes, but no bound for the minimum distance was given. In this work, we show how to derive quantum stabilizer codes with designed minimum distance from J-affine variety codes and their subfieldsubcodes. Moreover, this allows us to obtain new quantum codes, some of them either with better parameters, or with larger distances than the previously known codes.

引用

页数：32

共 51 条

[1] On quantum and classical BCH codes [J].

Aly, Salah A. ;

Klappenecker, Andreas ;

Sarvepalli, Pradeep Kiran .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2007, 53 (03) :1183-1188

[2] Evaluation codes from order domain theory [J].

Andersen, Henning E. ;

Geil, Olav .

FINITE FIELDS AND THEIR APPLICATIONS, 2008, 14 (01) :92-123

[3]

[Anonymous], SPRINGER INT SERIES

[4]

[Anonymous], P 2005 INT S INF THE

[5]

[Anonymous], LECT NOTES COMPUT SC

[6]

[Anonymous], BOUNDS MINIMUM DISTA

[7] Nonbinary quantum stabilizer codes [J].

Ashikhmin, A ;

Knill, E .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2001, 47 (07) :3065-3072

[8] Quantum error detection II: Bounds [J].

Ashikhmin, AE ;

Barg, AM ;

Knill, E ;

Litsyn, SN .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2000, 46 (03) :789-800

[9] Quantum error detection I: Statement of the problem [J].

Ashikhmin, AE ;

Barg, AM ;

Knill, E ;

Litsyn, SN .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2000, 46 (03) :778-788

[10]

Bierbrauer J, 2000, J COMB DES, V8, P174, DOI 10.1002/(SICI)1520-6610(2000)8:3<174::AID-JCD3>3.0.CO

← 1 2 3 4 5 6 →