On the Number of Cyclotomic Cosets and Cyclic Codes over Z13

Simple item page
dc.contributor.authorHussein, Lao
dc.contributor.authorKivunge, Benard
dc.contributor.authorKimani, Patrick
dc.contributor.authorMuthoka, Geoffrey
dc.date.accessioned2024-06-06T11:52:35Z
dc.date.available2024-06-06T11:52:35Z
dc.date.issued2018-06
dc.descriptionArticlesen_US
dc.description.abstractLet Zq be a finite field with q element and x n − 1 be a given cyclotomic polynomial. The number of cyclotomic cosets and cyclic codes has not been done in general. Although for different values of q the polynomial x n − 1 has been characterised. This paper will determine the number of irreducible monic polynomials and cyclotomic cosets of x n − 1 over Z13 .The factorization of x n − 1 over Z13 into irreducible polynomials using cyclotomic cosets of 13 modulo n will be established. The number of irreducible polynomials factors of x n − 1 over Zq is equal to the number of cyclotomic cosets of q modulo n. Each monic divisor of x n − 1 is a generator polynomial of cyclic code in Fq n . This paper will further show that the number of cyclic codes of length n over a finite field F is equal to the number of polynomials that divide x n − 1. Finally, the number of cyclic codes of length n, when n = 13k, n = 13k , n = 13k − 1, k, 13 = 1 are determine.en_US
dc.identifier.issnISSN: 2313-3759
dc.identifier.urihttp://repository.embuni.ac.ke/handle/embuni/4347
dc.language.isoenen_US
dc.publisherUoEmen_US
dc.relation.ispartofseriesVol. 5 No. 6;
dc.subjectcyclotomicen_US
dc.titleOn the Number of Cyclotomic Cosets and Cyclic Codes over Z13en_US
dc.typeArticleen_US
Files
Original bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
On the Number of Cyclotomic Cosets and Cyclic Codes over Z13.pdf
Size:
438.54 KB
Format:
Adobe Portable Document Format
Description:
Article
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.71 KB
Format:
Item-specific license agreed upon to submission
Description:
Download
Collections
Articles: Department of Mathematics and Statistics