Cyclic Codes via the General Two-Prime Generalized Cyclotomic Sequence of Order Two

Xia Zhou and Heng Liu

Journal of Mathematics, 2020, vol. 2020, 1-12

Abstract: 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.

Date: 2020
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2020/6625652.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2020/6625652.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6625652

DOI: 10.1155/2020/6625652

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().