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Cyclic Codes via the General Two-Prime Generalized Cyclotomic Sequence of Order Two
- Source :
- Journal of Mathematics, Vol 2020 (2020)
- Publication Year :
- 2020
- Publisher :
- Hindawi Limited, 2020.
-
Abstract
- Suppose that p and q are two distinct odd prime numbers with n = p q . In this paper, the uniform representation of general two-prime generalized cyclotomy with order two over ℤ n was demonstrated. Based on this general generalized cyclotomy, a type of binary sequences defined over F l was presented and their minimal polynomials and linear complexities were derived, where l = r s with a prime number r and gcd l , 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 F l 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.
- Subjects :
- Discrete mathematics
Sequence
Article Subject
General Mathematics
MathematicsofComputing_GENERAL
Prime number
Binary number
020206 networking & telecommunications
0102 computer and information sciences
02 engineering and technology
01 natural sciences
Uniform representation
Prime (order theory)
TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES
010201 computation theory & mathematics
0202 electrical engineering, electronic engineering, information engineering
QA1-939
Order (group theory)
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 23144785 and 23144629
- Volume :
- 2020
- Database :
- OpenAIRE
- Journal :
- Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....b8183b02550a4c67d1a9d700ecb1d0d5