Quantum Codes from Repeated-Root Cyclic and Negacyclic Codes of Length 4ps Over Fpm

被引：0

作者：

Rani, Saroj ^{[1
]}

Verma, Ram Krishna ^{[2
]}

Prakash, Om ^{[2
]}

机构：

[1] SA Jain PG Coll, Dept Math, Ambala 134003, India

[2] Indian Inst Technol, Dept Math, Patna 801106, Bihar, India

来源：

INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS | 2021年 / 60卷 / 04期

关键词：

Cyclic codes; Negacyclic codes; Repeated-root codes; Hamming distance; Quantum MDS codes; CONSTACYCLIC CODES; MDS CODES;

D O I：

10.1007/s10773-021-04757-5

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Let F-pm be a finite field with p(m) elements for an odd prime p and a positive integer m. In this paper, we aim to construct non-binary quantum codes from repeated root cyclic and negacyclic codes of length 4p(s) over F-pm. To achieve this, first we discuss the structure of all maximum distance separable (MDS) cyclic and negacyclic codes of length 4p(s) over F-pm and their Euclidean and Hermitian duals. Further, we establish a necessary and sufficient condition for these codes to contain their duals. Finally, many new and quantum MDS codes are obtained with the help of CSS and Hermitian constructions from dual containing cyclic and negacyclic codes.

引用

页码：1299 / 1327

页数：29

共 50 条

[1] Quantum MDS and synchronizable codes from cyclic and negacyclic codes of length 4ps over Fpm
Dinh, Hai Q.
Le, Ha T.
Nguyen, Bac T.
Tansuchat, Roengchai
QUANTUM INFORMATION PROCESSING, 2021, 20 (11)
[2] Cyclic and negacyclic codes of length 4ps over Fpm + uFpm
Dinh, Hai Q.
Sharma, Anuradha
Rani, Saroj
Sriboonchitta, Songsak
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2018, 17 (09)
[3] Negacyclic codes of length 4ps over Fpm + uFpm and their duals
Dinh, Hai Q.
Nguyen, Bac T.
Sriboonchitta, Songsak
DISCRETE MATHEMATICS, 2018, 341 (04) : 1055 - 1071
[4] Repeated-Root Cyclic and Negacyclic Codes of Length 6ps
Dinh, Hai Q.
RING THEORY AND ITS APPLICATIONS: RING THEORY SESSION IN HONOR OF T.Y. LAM ON HIS 70TH BIRTHDAY, 2014, 609 : 69 - 87
[5] Skew negacyclic codes of length 4ps over Fpm plus uFpm
Pathak, Sachin
Raj, Rishi
Maity, Dipendu
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2025,
[6] New quantum codes from negacyclic codes of length ps over Fpm + uFpm
Boudine, Brahim
Laaouine, Jamal
Charkani, Mohammed Elhassani
QUANTUM INFORMATION PROCESSING, 2023, 22 (01)
[7] On the Hamming distances of repeated-root constacyclic codes of length 4ps
Dinh, Hai Q.
Wang, Xiaoqiang
Liu, Hongwei
Sriboonchitta, Songsak
DISCRETE MATHEMATICS, 2019, 342 (05) : 1456 - 1470
[8] Quantum MDS and Synchronizable Codes From Cyclic and Negacyclic Codes of Length 2ps Over Fpm
Dinh, Hai Q.
Nguyen, Bac T.
Yamaka, Woraphon
IEEE ACCESS, 2020, 8 : 124608 - 124623
[9] On Hamming and b-symbol distance distributions of repeated-root constacyclic codes of length 4ps over Fpm + uFpm
Dinh, Hai Q.
Singh, Abhay Kumar
Thakur, Madhu Kant
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2021, 66 (1-2) : 885 - 905
[10] CYCLIC AND NEGACYCLIC CODES OF LENGTH 2ps OVER Fpm + uFpm
Liu, Xiusheng
Xu, Xiaofang
ACTA MATHEMATICA SCIENTIA, 2014, 34 (03) : 829 - 839

← 1 2 3 4 5 →