A DETAILED STUDY OF THE RELATIONSHIP BETWEEN SOME OF THE ROOT LATTICES AND THE CODING THEORY

IF 0.6 4区数学 Q3 MATHEMATICS

Kyushu Journal of Mathematics Pub Date : 2018-01-01 DOI:10.2206/KYUSHUJM.72.123

M. Ozeki

引用次数: 0

Abstract

Summary: In the present article we study the even unimodular lattice which lies between the root lattice m · A n and the dual lattice ( m · A n ) # . Here m · A n is an orthogonal sum of m copies of the root lattice A n . In the course of the study the code over the ring A # n /A n arises in a natural way. We ﬁnd that an intimate relationship between the even unimodular lattice containing m · A n as a sublattice and the error correcting code over the ring A # n /A n exists. As a consequence we could reconstruct sixteen non-isometric Niemeier lattices out of twenty-four non-isometric lattices by using the present approach.

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详细研究了一些根格与编码理论之间的关系

摘要:本文研究了介于根格m·n和对偶格(m·n) #之间的偶单模格。这里m·n是根晶格n的m个拷贝的正交和。在研究过程中，环上的代码a# n / an自然出现。我们发现含有m·A·n作为子格的偶单模格与环A # n /A n上的纠错码之间存在密切关系。结果表明，利用本方法可以从24个非等距尼迈耶晶格中重构出16个非等距尼迈耶晶格。

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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来源期刊

Kyushu Journal of Mathematics 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total. More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.