| 具有优良渐近参数的代数几何码 |
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| 引用本文： | 胡万宝. 具有优良渐近参数的代数几何码[J]. 数学杂志, 2007, 27(3): 271-275 |
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| 作者姓名： | 胡万宝 |
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| 作者单位： | 中国科学技术大学数学系,安徽合肥,230026;安庆师范学院数学系,安徽安庆,246011 |
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| 基金项目： | Acknowledgement I wish to thank professor Chaoping Xing from whom I have learnt more on the theory of A--G codes. |
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| 摘 要： | 本文讨论了一类具有好的渐近参数的代数几何码.通过对除子类数、高次有理除子数以及代数几何码的参数分析,得到一类码其渐近界优于Gilbert-Varshamov界和Xing界.在这两个界的交点处,渐近界有所改进.
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| 关 键 词： | 代数几何码 渐近参数 Gilbert-Varshamov界 Xing界 |
| 文章编号： | 0255-7797（2007）03-0271-05 |
| 修稿时间： | 2004-12-27 |
ALGEBRAIC GEOMETRY CODES WITH GOOD ASYMPTOTIC PARAMETERS |
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| HU Wan-bao. ALGEBRAIC GEOMETRY CODES WITH GOOD ASYMPTOTIC PARAMETERS[J]. Journal of Mathematics, 2007, 27(3): 271-275 |
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| Authors: | HU Wan-bao |
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| Abstract: | In this paper,we discuss a class of algebraic geometry codes (A-G codes) with good asymptotic parameters.Based on some analyses on a relation amony divisor class number, number of rational divisors of high degrees,and parameters of A-G codes,we obtain an asymptotic bound of a class, which is better than both the Gilbert-Varshamov and the Xing bounds.Our result shows that these two bounds can be improved significantly around the two points where they intersect. |
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| Keywords: | algebraic geometry codes asymptotic parameters Gilbert-Varshamov bound Xing bound |
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