Algebraic Decoding Techniques by Using Grobner Bases

使用 Grobner 基的代数解码技术

• 批准号: 9314347
• 负责人: Irving Reed
• 金额: $ 30.62万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-08-01 至 1997-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9314347&HistoricalAwards=false
• 关键词: Algebraic; Decoding; Techniques; Using; Grobner

9314347 Reed This is a program of research including four inter-related topics. (1) decoding techniques and Grobner bases: a polynomial point of view (2) decoding cyclic codes up to their true minimum distance, (3) decoding algebraic geometry codes, and (4) simplified decoding algorithms. The decoding problem will be formulated in terms of ideals, and relationships with the error locator polynomial and Grobner bases will be sought. Preliminary results show that is is possible to construct algebraic decoding methods by the use of Grobner bases to decode all cyclic codes up to the true minimum distance in some special cases. These techniques promise to be useful as a means of decoding algebraic geometry codes. Much effort in complexity analysis will be needed here. The overall goal is to come up with a low complexity decoding algorithm that corrects up to the true minimum distance. ***

9314347 REED这是一项研究计划，其中包括四个相互关联的主题。 （1）解码技术和grobner碱基：多项式的观点（2）将循环代码解码为其真实最小距离，（3）解码代数几何代码和（4）简化的解码算法。 解码问题将以理想的形式提出，并且将寻求与错误定位者多项式和Grobner碱基的关系。 初步结果表明，在某些特殊情况下，使用Grobner碱将所有循环代码解码为最小最小距离，可以通过使用Grobner碱来构建代数解码方法。 这些技术有望作为解码代数几何代码的一种手段。 这里需要大量的复杂性分析。 总体目标是提出一个低复杂性解码算法，该算法将校正到真正的最小距离。 ***