Gray images of the linear codes and their dual codes over F<sub>4</sub>+uF <sub>4</sub>
The linear codes over ring F<sub>4</sub>＋uF<sub>4</sub> and field F<sub>4</sub> were studied.By using the Gray weight w<sub>G</sub> ,the Gray distance d<sub>G</sub> of codes C over F<sub>4</sub>＋uF<sub>4</sub>,and th...
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| Format: | Article |
| Language: | zho |
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Editorial Department of Journal on Communications
2012-08-01
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| Series: | Tongxin xuebao |
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| Online Access: | http://www.joconline.com.cn/zh/article/doi/1000-436X(2012)08-0134-04/ |
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| _version_ | 1841539889220288512 |
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| author | Xiu-sheng LIU Hua-lu LIU |
| author_facet | Xiu-sheng LIU Hua-lu LIU |
| author_sort | Xiu-sheng LIU |
| collection | DOAJ |
| description | The linear codes over ring F<sub>4</sub>＋uF<sub>4</sub> and field F<sub>4</sub> were studied.By using the Gray weight w<sub>G</sub> ,the Gray distance d<sub>G</sub> of codes C over F<sub>4</sub>＋uF<sub>4</sub>,and the Gray map ψ from (F<sub>4</sub>＋uF<sub>4</sub>)<sup>n</sup> to <math display="block"> <mrow> <msubsup> <mi>F</mi> <mn>4</mn> <mrow> <mn>2</mn><mi>n</mi></mrow> </msubsup> </mrow></math>,the Gray image ψ(C)of linear codes C over F<sub>4</sub>＋uF<sub>4</sub> were linear codes over F <sub>4</sub> as well,d <sub>H</sub>(ψ(C))＝d <sub>G</sub>(C),and the proposition that linear codes ψ(C )⊥ were the dual codes of ψ(C) were showed.Furthermore,the Gray image ψ(C)of cyclic codes C over F<sub>4</sub>＋uF<sub>4</sub> were the 2-quasi cyclic codes over F<sub>4</sub>. |
| format | Article |
| id | doaj-art-04010397863543a691c4041b70b2e4f2 |
| institution | Kabale University |
| issn | 1000-436X |
| language | zho |
| publishDate | 2012-08-01 |
| publisher | Editorial Department of Journal on Communications |
| record_format | Article |
| series | Tongxin xuebao |
| spelling | doaj-art-04010397863543a691c4041b70b2e4f22025-01-14T06:32:52ZzhoEditorial Department of Journal on CommunicationsTongxin xuebao1000-436X2012-08-013313413759665016Gray images of the linear codes and their dual codes over F<sub>4</sub>+uF <sub>4</sub>Xiu-sheng LIUHua-lu LIUThe linear codes over ring F<sub>4</sub>＋uF<sub>4</sub> and field F<sub>4</sub> were studied.By using the Gray weight w<sub>G</sub> ,the Gray distance d<sub>G</sub> of codes C over F<sub>4</sub>＋uF<sub>4</sub>,and the Gray map ψ from (F<sub>4</sub>＋uF<sub>4</sub>)<sup>n</sup> to <math display="block"> <mrow> <msubsup> <mi>F</mi> <mn>4</mn> <mrow> <mn>2</mn><mi>n</mi></mrow> </msubsup> </mrow></math>,the Gray image ψ(C)of linear codes C over F<sub>4</sub>＋uF<sub>4</sub> were linear codes over F <sub>4</sub> as well,d <sub>H</sub>(ψ(C))＝d <sub>G</sub>(C),and the proposition that linear codes ψ(C )⊥ were the dual codes of ψ(C) were showed.Furthermore,the Gray image ψ(C)of cyclic codes C over F<sub>4</sub>＋uF<sub>4</sub> were the 2-quasi cyclic codes over F<sub>4</sub>.http://www.joconline.com.cn/zh/article/doi/1000-436X(2012)08-0134-04/linear codedual codeGray weightGray map |
| spellingShingle | Xiu-sheng LIU Hua-lu LIU Gray images of the linear codes and their dual codes over F<sub>4</sub>+uF <sub>4</sub> Tongxin xuebao linear code dual code Gray weight Gray map |
| title | Gray images of the linear codes and their dual codes over F<sub>4</sub>+uF <sub>4</sub> |
| title_full | Gray images of the linear codes and their dual codes over F<sub>4</sub>+uF <sub>4</sub> |
| title_fullStr | Gray images of the linear codes and their dual codes over F<sub>4</sub>+uF <sub>4</sub> |
| title_full_unstemmed | Gray images of the linear codes and their dual codes over F<sub>4</sub>+uF <sub>4</sub> |
| title_short | Gray images of the linear codes and their dual codes over F<sub>4</sub>+uF <sub>4</sub> |
| title_sort | gray images of the linear codes and their dual codes over f sub 4 sub uf sub 4 sub |
| topic | linear code dual code Gray weight Gray map |
| url | http://www.joconline.com.cn/zh/article/doi/1000-436X(2012)08-0134-04/ |
| work_keys_str_mv | AT xiushengliu grayimagesofthelinearcodesandtheirdualcodesoverfsub4subufsub4sub AT hualuliu grayimagesofthelinearcodesandtheirdualcodesoverfsub4subufsub4sub |