On the generalization of the construction of quantum codes from Hermitian self-orthogonal codes

被引：4

作者：

Galindo, Carlos ^{[1
,2
]}

Hernando, Fernando ^{[1
,2
]}

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

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2022年 / 90卷 / 05期

关键词：

Stabilizer quantum codes; Hermitian duality; Self-orthogonal codes; ERROR-CORRECTING CODES; MDS CODES; COMPUTATION;

D O I：

10.1007/s10623-022-01018-2

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Many q-ary stabilizer quantum codes can be constructed from Hermitian self-orthogonal q(2)-ary linear codes. This result can be generalized to q(2m)-ary linear codes, m > 1. We give a result for easily obtaining quantum codes from that generalization. As a consequence we provide several new binary stabilizer quantum codes which are records according to Grassl (Bounds on the minimum distance of linear codes, http://www.codetables.de, 2020) and new q-ary ones, with q not equal 2, improving others in the literature.

引用

页码：1103 / 1112

页数：10

共 50 条

[31] On construction of ternary optimal self-orthogonal codes
Li, Zhihao
Li, Ruihu
COMPUTATIONAL & APPLIED MATHEMATICS, 2024, 43 (03):
[32] On Shortening Construction of Self-orthogonal Quaternary Codes
Guo, Luobin
Fu, Qiang
Li, Ruihu
Li, Xueliang
2015 SEVENTH INTERNATIONAL WORKSHOP ON SIGNAL DESIGN AND ITS APPLICATIONS IN COMMUNICATIONS (IWSDA), 2015, : 99 - 102
[33] Constructing self-orthogonal and Hermitian self-orthogonal codes via weighing matrices and orbit matrices
Crnkovic, Dean
Egan, Ronan
Svob, Andrea
FINITE FIELDS AND THEIR APPLICATIONS, 2019, 55 : 64 - 77
[34] Three families of self-orthogonal codes and their application in optimal quantum codes
Li, Dexiang
Heng, Ziling
Li, Chengju
DISCRETE MATHEMATICS, 2023, 346 (12)
[35] Several Families of Self-Orthogonal Codes and Their Applications in Optimal Quantum Codes and LCD Codes
Wang, Xinran
Heng, Ziling
IEEE TRANSACTIONS ON INFORMATION THEORY, 2024, 70 (07) : 4769 - 4791
[36] Quantum codes derived from self-orthogonal codes over large finite rings
Lu, Huimin
Dong, Xuedong
Liu, Zhenxing
Zhang, Meili
2016 3RD INTERNATIONAL CONFERENCE ON INFORMATION SCIENCE AND CONTROL ENGINEERING (ICISCE), 2016, : 514 - 518
[37] Self-Orthogonal Codes From p-Divisible Codes
Li, Xiaoru
Heng, Ziling
IEEE TRANSACTIONS ON INFORMATION THEORY, 2024, 70 (12) : 8562 - 8586
[38] Binary Generalized Quasi-Cyclic Self-orthogonal Codes and Binary Construction of Pure Quantum Codes
Wang, Weiliang
Fan, Yangyu
Guo, Luobin
PROCEEDINGS OF THE 2014 INTERNATIONAL CONFERENCE ON FUTURE COMPUTER AND COMMUNICATION ENGINEERING, 2014, 111 : 142 - 145
[39] LCD codes and almost optimally extendable codes from self-orthogonal codes
Wang, Xinran
Heng, Ziling
Li, Fengwei
Yue, Qin
DESIGNS CODES AND CRYPTOGRAPHY, 2024, 92 (10) : 2901 - 2926
[40] Construction of binary and ternary self-orthogonal linear codes
Kohnert, Axel
Wassermann, Alfred
DISCRETE APPLIED MATHEMATICS, 2009, 157 (09) : 2118 - 2123

← 1 2 3 4 5 →