Optimal constructions of quantum and synchronizable codes from repeated-root cyclic codes of length 3ps

被引：0

作者：

Dinh, Hai Q. ^{[1
]}

Nguyen, Bac T. ^{[2
,3
]}

Paravee, M. ^{[4
]}

Thi, Hiep L. ^{[5
]}

Vo, Thang M. ^{[6
,7
]}

机构：

[1] Kent State Univ, Dept Math Sci, Kent, OH 44240 USA

[2] Duy Tan Univ, Inst Fundamental & Appl Sci, Ho Chi Minh City 700000, Vietnam

[3] Duy Tan Univ, Fac Nat Sci, Da Nang 550000, Vietnam

[4] Chiang Mai Univ, Fac Econ, Ctr Excellence Econometr, Chiang Mai 52000, Thailand

[5] Thu Dau Mot Univ, Fac Educ, Binh Duong, Vietnam

[6] Ind Univ Vinh, Dept Gen Educ, Vinh City, Nghe An, Vietnam

[7] Ohio Univ, Math Dept, Athens, OH 45701 USA

来源：

QUANTUM INFORMATION PROCESSING | 2023年 / 22卷 / 06期

关键词：

Cyclic codes; Repeated-root codes; Hamming distance; MDS codes; Quantum MDS codes; Quantum synchronizable codes; ERROR-CORRECTING CODES; CONSTACYCLIC CODES; MDS CODES; NEGACYCLIC CODES; EXPLICIT REPRESENTATION; ENTANGLEMENT; ENUMERATION; DISTANCE; 4P(S);

D O I：

10.1007/s11128-023-03958-7

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we use the CSS and Steane's constructions to establish quantum errorcorrecting codes (briefly, QEC codes) from cyclic codes of length 3p(s) over F-pm. We obtain several new classes of QEC codes in the sense that their parameters are different from all the previous constructions. Among them, we identify all quantum MDS (briefly, qMDS) codes, i.e., optimal quantum codes with respect to the quantum Singleton bound. In addition, we construct quantum synchronizable codes (briefly, QSCs) from cyclic codes of length 3p(s) over Fpm. Furthermore, we give many new QSC stoenrich the variety of available QSCs. Alot of them are QSCs codes with shorter lengths and much larger minimum distances than known non-primitive narrow-sense BCH codes.

引用

页数：25

共 50 条

[11] On Hamming distance distributions of repeated-root constacyclic codes of length 3ps over Fpm + uFpm
Dinh, Hai Q.
Nguyen, Bac T.
Thi, Hiep L.
Yamaka, Woraphon
DISCRETE MATHEMATICS, 2023, 346 (12)
[12] The Hamming distances of repeated-root cyclic codes of length 5ps
Li, Xia
Yue, Qin
Discrete Applied Mathematics, 2022, 284 : 29 - 41
[13] The Hamming distances of repeated-root cyclic codes of length 5ps
Li, Xia
Yue, Qin
DISCRETE APPLIED MATHEMATICS, 2020, 284 : 29 - 41
[14] On the Hamming Distance of Repeated-Root Cyclic Codes of Length 6ps
Dinh, Hai Q.
Wang, Xiaoqiang
Maneejuk, Paravee
IEEE ACCESS, 2020, 8 (08): : 39946 - 39958
[15] REPEATED-ROOT CYCLIC CODES
VANLINT, JH
IEEE TRANSACTIONS ON INFORMATION THEORY, 1991, 37 (02) : 343 - 345
[16] ON REPEATED-ROOT CYCLIC CODES
CASTAGNOLI, G
MASSEY, JL
SCHOELLER, PA
VONSEEMANN, N
IEEE TRANSACTIONS ON INFORMATION THEORY, 1991, 37 (02) : 337 - 342
[17] The minimum Hamming distances of repeated-root cyclic codes of length 6ps and their MDS codes
Gao, Ying
Yue, Qin
Li, Fengwei
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2021, 65 (1-2) : 107 - 123
[18] Explicit constructions of cyclic and negacyclic codes of length 3ps over Fpm
Phuto, Jirayu
Klin-Eam, Chakkrid
DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2020, 12 (05)
[19] Repeated-root constacyclic codes of length 2ps
Dinh, Hai Q.
FINITE FIELDS AND THEIR APPLICATIONS, 2012, 18 (01) : 133 - 143
[20] A NOTE ON REPEATED-ROOT CYCLIC CODES
MORELOSZARAGOZA, R
IEEE TRANSACTIONS ON INFORMATION THEORY, 1991, 37 (06) : 1736 - 1737

← 1 2 3 4 5 →