Good p-ary quasic-cyclic codes from cyclic codes over $$\mathbb{F}_ p + v\mathbb{F}_ p$$ |
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| Authors: | Minjia Shi Shanlin Yang Shixin Zhu |
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| Institution: | Minjia SHI, School of Mathematical Sciences,Anhui University,Hefei 230601,China. Shanlin YANG Institute of Computer Network Systems,Hefei University of Technology,Hefei 230009,China. Shixin ZHU School of Mathematical Sciences,Hefei University of Technology,Hefei 230009,China. |
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| Abstract: | This paper introduces a Gray map from
( \mathbbFp + v\mathbbFp )n\left( {\mathbb{F}_p + v\mathbb{F}_p } \right)^n to
\mathbbFp2n\mathbb{F}_p^{2n}, and describes the relationship between codes over
\mathbbFp + v\mathbbFp\mathbb{F}_p + v\mathbb{F}_p and their Gray images. The authors prove that every cyclic code of arbitrary length n over
\mathbbFp + v\mathbbFp\mathbb{F}_p + v\mathbb{F}_p is principal, and determine its generator polynomial as well as the number of cyclic codes. Moreover, the authors obtain
many best-known p-ary quasic-cyclic codes in terms of their parameters via the Gray map. |
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