The structure of one weight linear and cyclic codes over Z_{2}^r x (Z_{2} + uZ_{2})^s
Inspired by the Z2Z4-additive codes, linear codes over Z_{2}^r x (Z_{2} + uZ_{2})^s have been introduced by Aydogdu et al. more recently. Although these family of codes are similar to each other, linear codes over Z_{2}^r x (Z_{2} + uZ_{2})^s have some advantages compared to Z2Z4-additive codes. A...
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| Format: | Article |
| Language: | English |
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Balikesir University
2017-12-01
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| Series: | An International Journal of Optimization and Control: Theories & Applications |
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| Online Access: | http://ijocta.org/index.php/files/article/view/512 |
| _version_ | 1797922426073382912 |
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| author | Ismail Aydogdu |
| author_facet | Ismail Aydogdu |
| author_sort | Ismail Aydogdu |
| collection | DOAJ |
| description | Inspired by the Z2Z4-additive codes, linear codes over Z_{2}^r x (Z_{2} + uZ_{2})^s have been introduced by Aydogdu et al. more recently. Although these family of codes are similar to each other, linear codes over Z_{2}^r x (Z_{2} + uZ_{2})^s have some advantages compared to Z2Z4-additive codes. A code is called constant weight(one weight) if all the codewords have the same weight. It is well known that constant weight or one weight codes have many important applications. In this paper, we study the structure of one weight Z2Z2[u]-linear and cyclic codes. We classify these type of one weight codes and also give some illustrative examples. |
| first_indexed | 2024-04-10T14:32:13Z |
| format | Article |
| id | doaj.art-ee0147cf86fa48239ef29b7049e402ce |
| institution | Directory Open Access Journal |
| issn | 2146-0957 2146-5703 |
| language | English |
| last_indexed | 2024-04-10T14:32:13Z |
| publishDate | 2017-12-01 |
| publisher | Balikesir University |
| record_format | Article |
| series | An International Journal of Optimization and Control: Theories & Applications |
| spelling | doaj.art-ee0147cf86fa48239ef29b7049e402ce2023-02-15T16:08:48ZengBalikesir UniversityAn International Journal of Optimization and Control: Theories & Applications2146-09572146-57032017-12-018110.11121/ijocta.01.2018.00512The structure of one weight linear and cyclic codes over Z_{2}^r x (Z_{2} + uZ_{2})^sIsmail Aydogdu0Yildiz Technical UniversityInspired by the Z2Z4-additive codes, linear codes over Z_{2}^r x (Z_{2} + uZ_{2})^s have been introduced by Aydogdu et al. more recently. Although these family of codes are similar to each other, linear codes over Z_{2}^r x (Z_{2} + uZ_{2})^s have some advantages compared to Z2Z4-additive codes. A code is called constant weight(one weight) if all the codewords have the same weight. It is well known that constant weight or one weight codes have many important applications. In this paper, we study the structure of one weight Z2Z2[u]-linear and cyclic codes. We classify these type of one weight codes and also give some illustrative examples.http://ijocta.org/index.php/files/article/view/512One weight codesZ2Z2[u]-linear codesduality. |
| spellingShingle | Ismail Aydogdu The structure of one weight linear and cyclic codes over Z_{2}^r x (Z_{2} + uZ_{2})^s An International Journal of Optimization and Control: Theories & Applications One weight codes Z2Z2[u]-linear codes duality. |
| title | The structure of one weight linear and cyclic codes over Z_{2}^r x (Z_{2} + uZ_{2})^s |
| title_full | The structure of one weight linear and cyclic codes over Z_{2}^r x (Z_{2} + uZ_{2})^s |
| title_fullStr | The structure of one weight linear and cyclic codes over Z_{2}^r x (Z_{2} + uZ_{2})^s |
| title_full_unstemmed | The structure of one weight linear and cyclic codes over Z_{2}^r x (Z_{2} + uZ_{2})^s |
| title_short | The structure of one weight linear and cyclic codes over Z_{2}^r x (Z_{2} + uZ_{2})^s |
| title_sort | structure of one weight linear and cyclic codes over z 2 r x z 2 uz 2 s |
| topic | One weight codes Z2Z2[u]-linear codes duality. |
| url | http://ijocta.org/index.php/files/article/view/512 |
| work_keys_str_mv | AT ismailaydogdu thestructureofoneweightlinearandcycliccodesoverz2rxz2uz2s AT ismailaydogdu structureofoneweightlinearandcycliccodesoverz2rxz2uz2s |