Cyclic Codes via the General Two-Prime Generalized Cyclotomic Sequence of Order Two
Author
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-12-23
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
Suppose that p and q are two distinct odd prime numbers with n=pq.
In this paper, the uniform representation of general two-prime generalized cyclotomy with order two over ℤn was demonstrated.
Based on this general generalized cyclotomy, a type of binary sequences defined over Fl was presented and their minimal polynomials and linear complexities were derived, where l=rs with a prime number r and gcdl,n=1.
The results have indicated that the linear complexities of these sequences are high without any special requirements on the prime numbers.
Furthermore, we employed these sequences to obtain a few cyclic codes over Fl with length n and developed the lower bounds of the minimum distances of many cyclic codes.
It is important to stress that some cyclic codes in this paper are optimal.
American Psychological Association (APA)
Zhou, Xia. 2020. Cyclic Codes via the General Two-Prime Generalized Cyclotomic Sequence of Order Two. Journal of Mathematics،Vol. 2020, no. 2020, pp.1-12.
https://search.emarefa.net/detail/BIM-1188112
Modern Language Association (MLA)
Zhou, Xia. Cyclic Codes via the General Two-Prime Generalized Cyclotomic Sequence of Order Two. Journal of Mathematics No. 2020 (2020), pp.1-12.
https://search.emarefa.net/detail/BIM-1188112
American Medical Association (AMA)
Zhou, Xia. Cyclic Codes via the General Two-Prime Generalized Cyclotomic Sequence of Order Two. Journal of Mathematics. 2020. Vol. 2020, no. 2020, pp.1-12.
https://search.emarefa.net/detail/BIM-1188112
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1188112