Open Access
Research Article
Exponent of cyclic codes over
*N. AnnamalaiCorresponding authoralgebra.annamalai@gmail.comDepartment of Computational Science and HumanitiesPala 686635, KeralaIndian Institute of Information Technology KottayamIndiaView full profile → , Durairajan Chinnapillaicdurai66@rediffmail.comDepartment of MathematicsSchool of Mathematical SciencesTiruchirappalli 620024, Tamil NaduBharathidasan UniversityIndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 31 Aug 2020
- Accepted:
- 31 Jan 2021
- Published Online:
- 02 Aug 2021
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-1314
- Pages:
- 115–120
Abstract
In this paper, we introduce the exponent of a cyclic code over the finite field with q = pm elements. Also, we prove that the exponent of the dual of cyclic code satisfies the condition n = lcm(e, r) where n is the length of the cyclic code, e = exp(C) and r = exp(C⊥ ).
Keywords
Subject Classifications
(2010) 94B0594B1594B25
References
- David S. Dummit and Richard M. Foote, Abstract Algebra, Wiley; 3rd Edition, July 14, 2003. [Google Scholar]
- Manju Pruthi and Sunil Kumar, Cyclic codes with generalized cyclotomic cubic classes, Journal of Discrete Mathematical Sciences and Cryptography, 22:6, 923-933(2019), DOI: 10.1080/09720529.2019.1627706. [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
- Pankaj and Manju Pruthi, Cyclic codes from Whiteman’s generalized cyclotomic sequences of order 2r, r ≥ 2, Journal of Information and Optimization Sciences, 38:3-4, 621-646(2017), DOI: 10.1080/02522667.2017.1303948. [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
- Pankaj and Manju Pruthi, Cyclic codes of prime power length from generalized cyclotomic classes of order 2r, Journal of Information and Optimization Sciences, 39:4, 965-971(2018), DOI: 10.1080/02522667.2018.1460136. [Taylor & Francis Online], [Web of Science ®], [Google Scholar]
- Rudolf Lidl and Harald Niederreiter, Introduction to finite fields and their applications, Cambridge University press, Cambridge, 1986. [Google Scholar]
- Vera Pless, Introduction to the Theory of Error-Correcting Codes, John Wiley & Sons, Inc, 1998. [Crossref], [Google Scholar]
Views: 72Downloads: 26Citations: 0
