Binary Generalized Quasi-Cyclic Self-orthogonal Codes and Binary Construction of Pure Quantum Codes

被引：0
作者：
Wang, Weiliang [1 ,2 ]
Fan, Yangyu [1 ]
Guo, Luobin [2 ]
机构：
[1] Sch Elect & Informat, Northwestern Polytech, Xian, Peoples R China
[2] AF Engn Univ, Coll Sci, Xian, Peoples R China
来源：
PROCEEDINGS OF THE 2014 INTERNATIONAL CONFERENCE ON FUTURE COMPUTER AND COMMUNICATION ENGINEERING | 2014年 / 111卷
基金：
中国国家自然科学基金;
关键词：
Quantum code; Steane construction; self-orthogonal code; generalized quasi-cyclic code; pair of nested self-orthogonal codes; ERROR-CORRECTING CODES; STRUCTURAL-PROPERTIES; ALGEBRAIC STRUCTURE;
D O I：
暂无
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In this paper, a special subclass of binary generalized quasi-cyclic self-orthogonal codes and quantum codes constructed by Steane construction are discussed. Firstly, eight 16-dimensional even length generalized quasi-cyclic self-orthogonal codes with dual distance five are built based on circulant or partial circulant matrices. Secondly, pairs of nested self-orthogonal codes with dual distance five and three are designed by applying an algorithm for searching subcodes of a given code. Thirdly, revised pairs of codes with dual distance six and four are constructed by extending previous pairs of codes, and then eight quantum codes with distance six are obtained by Steane construction. These eight quantum codes are new binary construction by Steane construction and are best known ones.
引用
收藏
页码：142 / 145
页数：4
相关论文
共 50 条
[21]   SKEW GENERALIZED QUASI-CYCLIC CODES [J].
Abualrub, Taher ;
Ezerman, Martianus Frederic ;
Seneviratne, Padmapani ;
Sole, Patrick .
TWMS JOURNAL OF PURE AND APPLIED MATHEMATICS, 2018, 9 (02) :123-134
[22]   On the Construction of Skew Quasi-Cyclic Codes [J].
Abualrub, Taher ;
Ghrayeb, Ali ;
Aydin, Nuh ;
Siap, Irfan .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2010, 56 (05) :2081-2090
[23]   Generalized quasi-cyclic codes: structural properties and code construction [J].
M. Esmaeili ;
S. Yari .
Applicable Algebra in Engineering, Communication and Computing, 2009, 20 :159-173
[24]   A Modulus Factorization Algorithm for Self-Orthogonal and Self-Dual Quasi-Cyclic Codes via Polynomial Matrices [J].
Matsui, Hajime .
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2021, E104A (11) :1649-1653
[25]   Binary construction of pure additive quantum codes with distance five or six [J].
YangYu Fan ;
WeiLiang Wang ;
RuiHu Li .
Quantum Information Processing, 2015, 14 :183-200
[26]   Three families of self-orthogonal codes and their application in optimal quantum codes [J].
Li, Dexiang ;
Heng, Ziling ;
Li, Chengju .
DISCRETE MATHEMATICS, 2023, 346 (12)
[27]   Quasi-cyclic constructions of quantum codes [J].
Galindo, Carlos ;
Hernando, Fernando ;
Matsumoto, Ryutaroh .
FINITE FIELDS AND THEIR APPLICATIONS, 2018, 52 :261-280
[28]   A new construction of quantum codes from quasi-cyclic codes over finite fields [J].
Biswas, Soumak ;
Bhaintwal, Maheshanand .
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2023, 54 (02) :375-388
[29]   Generalized Quasi-Cyclic Codes with Arbitrary Block Lengths [J].
Muchtadi-Alamsyah, Intan ;
Irwansyah ;
Barra, Aleams .
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2022, 45 (03) :1383-1407
[30]   Self-orthogonal cyclic codes with good parameters [J].
Zhang, Jiayuan ;
Kai, Xiaoshan ;
Li, Ping .
FINITE FIELDS AND THEIR APPLICATIONS, 2025, 101
12345