• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Designs, Codes and Crytography >Lexicodes over finite principal ideal rings
【24h】

Lexicodes over finite principal ideal rings

机译：有限主理想环上的Lexicodes

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Let R be a (possibly noncommutative) finite principal ideal ring. Via a total ordering of the ring elements and an ordered basis a lexicographic ordering of the module R-n is produced. This is used to set up a greedy algorithm that selects vectors for which all linear combinations with the previously selected vectors satisfy a pre-specified selection property and updates the to-be-constructed code to the linear hull of the vectors selected so far. The output is called a lexicode. This process was discussed earlier in the literature for fields and chain rings. In this paper we investigate the properties of such lexicodes over finite principal ideal rings and show that the total ordering of the ring elements has to respect containment of ideals for the algorithm to produce meaningful results. Only then it is guaranteed that the algorithm is exhaustive and thus produces codes that are maximal with respect to inclusion. It is further illustrated that the output of the algorithm heavily depends on the total ordering and chosen basis.
机译：令R为（可能是非交换的）有限主体理想环。通过环元素的总排序和有序的基础，生成模块R-n的字典顺序。这用于建立贪婪算法，该贪婪算法选择与先前选择的向量的所有线性组合都满足预定选择属性的向量，并将待构造的代码更新为到目前为止选择的向量的线性外壳。输出称为lexicode。这个过程在前面的领域和链环文献中已有讨论。在本文中，我们研究了有限主理想环上此类列线的性质，并表明，环元素的总排序必须考虑理想的约束，才能使算法产生有意义的结果。只有这样才能保证算法是穷举性的，并因此产生关于包含的最大代码。进一步说明，算法的输出很大程度上取决于总的排序和选择的基础。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号