On the structure of cyclic codes over the ring Z<inf>2<sup>s</sup></inf>[u]∕〈u<sup>k</sup>〉
© 2018 Elsevier B.V. In this paper, we consider cyclic codes of odd length n over the local, non-chain ring R=Z2s[u]∕〈uk〉 = Z2s+uZ2s+…+uk−1Z2s(uk=0), for any integers s≥1 and k≥2. An explicit algebraic representation of such codes is obtained. This algebraic structure is then used to establish the d...
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th-cmuir.6653943832-587972018-09-05T04:32:26Z On the structure of cyclic codes over the ring Z<inf>2<sup>s</sup></inf>[u]∕〈u<sup>k</sup>〉 Hai Q. Dinh Abhay Kumar Singh Pratyush Kumar Songsak Sriboonchitta Mathematics © 2018 Elsevier B.V. In this paper, we consider cyclic codes of odd length n over the local, non-chain ring R=Z2s[u]∕〈uk〉 = Z2s+uZ2s+…+uk−1Z2s(uk=0), for any integers s≥1 and k≥2. An explicit algebraic representation of such codes is obtained. This algebraic structure is then used to establish the duals of all cyclic codes. Among others, all self-dual cyclic codes of odd length n over the ring R are determined. Moreover, some examples are provided which produce several optimal codes. 2018-09-05T04:32:26Z 2018-09-05T04:32:26Z 2018-08-01 Journal 0012365X 2-s2.0-85047331677 10.1016/j.disc.2018.04.028 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85047331677&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/58797 |
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Mathematics Hai Q. Dinh Abhay Kumar Singh Pratyush Kumar Songsak Sriboonchitta On the structure of cyclic codes over the ring Z<inf>2<sup>s</sup></inf>[u]∕〈u<sup>k</sup>〉 |
| description |
© 2018 Elsevier B.V. In this paper, we consider cyclic codes of odd length n over the local, non-chain ring R=Z2s[u]∕〈uk〉 = Z2s+uZ2s+…+uk−1Z2s(uk=0), for any integers s≥1 and k≥2. An explicit algebraic representation of such codes is obtained. This algebraic structure is then used to establish the duals of all cyclic codes. Among others, all self-dual cyclic codes of odd length n over the ring R are determined. Moreover, some examples are provided which produce several optimal codes. |
| 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 |
On the structure of cyclic codes over the ring Z<inf>2<sup>s</sup></inf>[u]∕〈u<sup>k</sup>〉 |
| title_short |
On the structure of cyclic codes over the ring Z<inf>2<sup>s</sup></inf>[u]∕〈u<sup>k</sup>〉 |
| title_full |
On the structure of cyclic codes over the ring Z<inf>2<sup>s</sup></inf>[u]∕〈u<sup>k</sup>〉 |
| title_fullStr |
On the structure of cyclic codes over the ring Z<inf>2<sup>s</sup></inf>[u]∕〈u<sup>k</sup>〉 |
| title_full_unstemmed |
On the structure of cyclic codes over the ring Z<inf>2<sup>s</sup></inf>[u]∕〈u<sup>k</sup>〉 |
| title_sort |
on the structure of cyclic codes over the ring z<inf>2<sup>s</sup></inf>[u]∕〈u<sup>k</sup>〉 |
| publishDate |
2018 |
| url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85047331677&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/58797 |
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