| 关于两个特殊环曲面码的参数 |
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| 引用本文： | 左怀青,张平,罗雪.关于两个特殊环曲面码的参数[J].数学年刊A辑(中文版),2010,31(5):517-524. |
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| 作者姓名： | 左怀青 张平 罗雪 |
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| 作者单位： | 华东师范大学数学系;Department of Mathematics Statistics and Computer Sciences;University of Illinois at Chicago;重庆大学数学与统计学院数学系; |
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| 摘 要： | 扩充了Hansen的关于几个环曲面码的结果,给出两个新的环曲面码,并且用上同调的方法来计算码的维数,用相交理论的方法来估计最小距离,主要目的是为了证明对应两个不同的多边形可能具有相同的参数.最后,证明了这些新的码在某些有限域上是最好的码.
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| 关 键 词： | 代数几何码 环曲面码 环代数簇 |
On the Parameters of Two Special Toric Surface Codes |
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| ZUO Huaiqing,ZHANG Ping and LUO Xue.On the Parameters of Two Special Toric Surface Codes[J].Chinese Annals of Mathematics,2010,31(5):517-524. |
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| Authors: | ZUO Huaiqing ZHANG Ping and LUO Xue |
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| Institution: | ZUO Huaiqing~1 ZHANG Ping~2 LUO Xue~1 1 Department of Mathematics,East China Normal University,Shanghai 200241,China.Department of Mathematics,Statistics and Computer Science,University of Illinois at Chicago,Chicago,Illinois 60607,USA. 2 Department of Mathematics,College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China. |
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| Abstract: | The authors expand the results of J.Hansen and give two new Toric surface codes,calculate the dimension of the code by using the methods of cohomology and estimate the minimum distance relying on the intersection theory.The main purpose of the present paper is to show that the two codes corresponding two different polygons may have the same parameters.At last,the result that these new codes are the best at some finite field is also shown. |
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| Keywords: | Algebraic-geometry codes Toric surface codes Toric variety |
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