高斯整数上完备李码的推广

2006 IEEE International Symposium on Information Theory Pub Date : 2006-07-09 DOI:10.1109/ISIT.2006.261892

C. Martínez, Miquel Moretó, R. Beivide, E. Gabidulin

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引用次数: 13

摘要

本文给出了由广义高斯图导出的二维星座的完美编码，广义高斯图是建立在高斯整数商环上的一类图。利用广义高斯图的距离，我们解决了寻找t支配集的问题，并在这些图上建立了新的完美码。众所周知的完美李氏码可以看作是本文介绍的完美高斯码的一个特殊子情况

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Generalization of Perfect Lee Codes over Gaussian Integers

In this paper we present perfect codes for two-dimensional constellations derived from generalized Gaussian graphs, a family of graphs built over quotient rings of Gaussian integers. Using the generalized Gaussian graphs distance, we solve the problem of finding t-dominating sets and, then, we build new perfect codes over these graphs. The well-known perfect Lee codes can be viewed as a particular subcase of the perfect Gaussian codes introduced in this work

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2006 IEEE International Symposium on Information Theory

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