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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| Main Authors: | , |
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| Format: | Article |
| Language: | zho |
| Published: |
Editorial Department of Journal on Communications
2012-08-01
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| Series: | Tongxin xuebao |
| Subjects: | |
| Online Access: | http://www.joconline.com.cn/zh/article/doi/1000-436X(2012)08-0134-04/ |
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| Summary: | 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>. |
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| ISSN: | 1000-436X |