The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
본 논문에서는 인덱스 2를 갖는 70-생성기 QT(Quasi-Twisted) 코드의 특별한 클래스가 제시됩니다. 우리는 QT 코드 클래스의 대수적 구조와 Hermitian 이중 코드의 형태를 탐구합니다. 에르미트 내적과 자기 직교성을 위한 충분조건이 유도된다. Hermitian 자기 직교 QT 코드 클래스를 사용하여 두 개의 새로운 이진 양자 코드 [[42, 7, XNUMX]]를 구성합니다.2, [[78, 30, 10]]2. Ref.[6]의 정리 2에 따르면, 9개의 새로운 이진 양자 코드를 추가로 얻을 수 있습니다. 따라서 총 11개의 새로운 이진 양자 코드가 얻어지고 양자 길버트-바르샤모프(GV) 경계를 깨뜨릴 수 있는 10개의 양자 코드가 있습니다.
Yu YAO
Air Force Engineering University
Yuena MA
Air Force Engineering University
Jingjie LV
Air Force Engineering University
Hao SONG
Air Force Engineering University
Qiang FU
Air Force Engineering University
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Yu YAO, Yuena MA, Jingjie LV, Hao SONG, Qiang FU, "New Binary Quantum Codes Derived from Quasi-Twisted Codes with Hermitian Inner Product" in IEICE TRANSACTIONS on Fundamentals,
vol. E104-A, no. 12, pp. 1718-1722, December 2021, doi: 10.1587/transfun.2021EAL2030.
Abstract: In this paper, a special class of two-generator quasi-twisted (QT) codes with index 2 will be presented. We explore the algebraic structure of the class of QT codes and the form of their Hermitian dual codes. A sufficient condition for self-orthogonality with Hermitian inner product is derived. Using the class of Hermitian self-orthogonal QT codes, we construct two new binary quantum codes [[70, 42, 7]]2, [[78, 30, 10]]2. According to Theorem 6 of Ref.[2], we further can get 9 new binary quantum codes. So a total of 11 new binary quantum codes are obtained and there are 10 quantum codes that can break the quantum Gilbert-Varshamov (GV) bound.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021EAL2030/_p
부
@ARTICLE{e104-a_12_1718,
author={Yu YAO, Yuena MA, Jingjie LV, Hao SONG, Qiang FU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={New Binary Quantum Codes Derived from Quasi-Twisted Codes with Hermitian Inner Product},
year={2021},
volume={E104-A},
number={12},
pages={1718-1722},
abstract={In this paper, a special class of two-generator quasi-twisted (QT) codes with index 2 will be presented. We explore the algebraic structure of the class of QT codes and the form of their Hermitian dual codes. A sufficient condition for self-orthogonality with Hermitian inner product is derived. Using the class of Hermitian self-orthogonal QT codes, we construct two new binary quantum codes [[70, 42, 7]]2, [[78, 30, 10]]2. According to Theorem 6 of Ref.[2], we further can get 9 new binary quantum codes. So a total of 11 new binary quantum codes are obtained and there are 10 quantum codes that can break the quantum Gilbert-Varshamov (GV) bound.},
keywords={},
doi={10.1587/transfun.2021EAL2030},
ISSN={1745-1337},
month={December},}
부
TY - JOUR
TI - New Binary Quantum Codes Derived from Quasi-Twisted Codes with Hermitian Inner Product
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1718
EP - 1722
AU - Yu YAO
AU - Yuena MA
AU - Jingjie LV
AU - Hao SONG
AU - Qiang FU
PY - 2021
DO - 10.1587/transfun.2021EAL2030
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E104-A
IS - 12
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - December 2021
AB - In this paper, a special class of two-generator quasi-twisted (QT) codes with index 2 will be presented. We explore the algebraic structure of the class of QT codes and the form of their Hermitian dual codes. A sufficient condition for self-orthogonality with Hermitian inner product is derived. Using the class of Hermitian self-orthogonal QT codes, we construct two new binary quantum codes [[70, 42, 7]]2, [[78, 30, 10]]2. According to Theorem 6 of Ref.[2], we further can get 9 new binary quantum codes. So a total of 11 new binary quantum codes are obtained and there are 10 quantum codes that can break the quantum Gilbert-Varshamov (GV) bound.
ER -