Cyclic codes over the ring GR(p<sup>e</sup>,m)[u]∕〈u<sup>k</sup>〉
© 2019 Elsevier B.V. Let R=GR(pe,m)[u]∕〈uk〉 be a finite commutative ring for a prime p and any positive integers e,m and k. In this paper, we derive the explicit representation of cyclic codes over the ring R of length n, where n and p are coprime. We also discuss the dual of such cyclic codes over...
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th-cmuir.6653943832-657042019-08-05T04:39:49Z Cyclic codes over the ring GR(p<sup>e</sup>,m)[u]∕〈u<sup>k</sup>〉 Hai Q. Dinh Abhay Kumar Singh Pratyush Kumar Songsak Sriboonchitta Mathematics © 2019 Elsevier B.V. Let R=GR(pe,m)[u]∕〈uk〉 be a finite commutative ring for a prime p and any positive integers e,m and k. In this paper, we derive the explicit representation of cyclic codes over the ring R of length n, where n and p are coprime. We also discuss the dual of such cyclic codes over the ring R and give a sufficient condition for the codes to be self-dual. Moreover, we study quasi-cyclic codes of length kn and index k over the ring R, and obtain some good codes satisfying the bound given in Dougherty and Shiromoto (2000) over the ring Z9 as an example. 2019-08-05T04:39:49Z 2019-08-05T04:39:49Z 2019-01-01 Journal 0012365X 2-s2.0-85068585212 10.1016/j.disc.2019.05.036 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85068585212&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/65704 |
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Mathematics |
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Mathematics Hai Q. Dinh Abhay Kumar Singh Pratyush Kumar Songsak Sriboonchitta Cyclic codes over the ring GR(p<sup>e</sup>,m)[u]∕〈u<sup>k</sup>〉 |
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© 2019 Elsevier B.V. Let R=GR(pe,m)[u]∕〈uk〉 be a finite commutative ring for a prime p and any positive integers e,m and k. In this paper, we derive the explicit representation of cyclic codes over the ring R of length n, where n and p are coprime. We also discuss the dual of such cyclic codes over the ring R and give a sufficient condition for the codes to be self-dual. Moreover, we study quasi-cyclic codes of length kn and index k over the ring R, and obtain some good codes satisfying the bound given in Dougherty and Shiromoto (2000) over the ring Z9 as an example. |
| format |
Journal |
| author |
Hai Q. Dinh Abhay Kumar Singh Pratyush Kumar Songsak Sriboonchitta |
| author_facet |
Hai Q. Dinh Abhay Kumar Singh Pratyush Kumar Songsak Sriboonchitta |
| author_sort |
Hai Q. Dinh |
| title |
Cyclic codes over the ring GR(p<sup>e</sup>,m)[u]∕〈u<sup>k</sup>〉 |
| title_short |
Cyclic codes over the ring GR(p<sup>e</sup>,m)[u]∕〈u<sup>k</sup>〉 |
| title_full |
Cyclic codes over the ring GR(p<sup>e</sup>,m)[u]∕〈u<sup>k</sup>〉 |
| title_fullStr |
Cyclic codes over the ring GR(p<sup>e</sup>,m)[u]∕〈u<sup>k</sup>〉 |
| title_full_unstemmed |
Cyclic codes over the ring GR(p<sup>e</sup>,m)[u]∕〈u<sup>k</sup>〉 |
| title_sort |
cyclic codes over the ring gr(p<sup>e</sup>,m)[u]∕〈u<sup>k</sup>〉 |
| publishDate |
2019 |
| url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85068585212&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/65704 |
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