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    188宝金博页面版: On the Characterization of Cyclic Co des over Ring F2 uF2 v F2

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    内容提示： Chin. Quart. J. of Math.2014, 29 (2): 210—214On the Characterization of CyclicCodes over Ring F2+ uF2+ vF2ZHANG Xiao-yan(School of Mathematics and Physics, Hubei Polytechnic University, Huangshi 435003, China)Abstract: In this work, we investigate the cyclic codes over the ring F2 + uF2 + vF2. Wefirst study the relationship between linear codes over F2 + uF2 + vF2 and that over F2.Then we give a characterization of the cyclic codes over F2+ uF2+ vF2. Finally, we obtainthe number of the cyclic code over F2...

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    Chin. Quart. J. of Math.2014, 29 (2): 210—214On the Characterization of CyclicCodes over Ring F2+ uF2+ vF2ZHANG Xiao-yan(School of Mathematics and Physics, Hubei Polytechnic University, Huangshi 435003, China)Abstract: In this work, we investigate the cyclic codes over the ring F2 + uF2 + vF2. Wefirst study the relationship between linear codes over F2 + uF2 + vF2 and that over F2.Then we give a characterization of the cyclic codes over F2+ uF2+ vF2. Finally, we obtainthe number of the cyclic code over F2 + uF2 + vF2 of length n.Key words: linear code; cyclic code; Gray map; generator matrix2000 MR Subject Classification: 94B05, 94A15CLC number: O157.4Document code: AArticle ID: 1002–0462 (2014) 02–0210–05§1.IntroductionIn 1994, Hammons et al[1]studied how to construct some nonlinear codes by applyingthe Gray map to cyclic codes over Z4. Since then the study of cyclic codes over rings hasgreatly intensified, many papers have dealt with cyclic codes over various types rings(see [4-6]).Recently, cyclic codes over the ring F2+ uF2+ vF2+ uvF2 have been considered by Yildizand Karadeniz in [2], where some good binary codes have been obtained as the images undertwo Gray maps. Some results about cyclic codes over F2+ vF2were given by Zhu et al in [3],where it is shown that cyclic codes over the ring are principally generated.In this work, we will let R denote F2+ uF2+ vF2, where u2= uv = vu = 0, v2= v. Thering R is a finite principal ideal ring, i.e., R is a finite Frobenius ring, not a finite chain ring.We first define a Gray map from Rnto F3nof length n under the Gray map is a distance-invariant linear code over F2of length 3n. Using2, and prove that the image of a linear code over RReceived date: 2012-06-25Foundation item: Supported by the Scientific Research Foundation of Education Department of HubeiProvince(B2013069); Supported by the National Science Foundation of Hubei Polytechnic University ofChina(12xjz14A, 11yjz37B)Biography: ZHANG Xiao-yan(1979-), female, native of Huangshi, Hubei, an associate professor of HubeiPolytechnic University, engages in algebra coding.

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