A new construction of lattices from codes over GF(3)
A new construction of lattices from codes over GF(3)
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基于 GF(3) 的代码的新格构造
DOI：
10.1016/0012-365x(93)e0088-l
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
Paul Montague
中科院分区：
文献类型：
--
作者：
Paul Montague
我们从特定的长三元线性码中定义了一对d维z晶格的构造ford= 0 mod 24，它补充了由Sloane（1979）和Conway and Sloane（1988）的工作的扩展所给出的d维爱森斯坦晶格的构造（从而补充了2d维z晶格）。我们证明了这些结构在长度为24的自对偶码的情况下产生所有的尼迈耶格，通过类比先前关于二进制码的工作，表明与物理学中自对偶共形场论的分类问题相关。此外，我们的中间结果与长度为24的自对偶三进制码的分类有关。
We define a pair of constructions ofd-dimensional Z-lattices ford= 0 mod 24 from particular lengthdternary linear codes, which supplement the construction ofd-dimensional Eisenstein lattices (and hence 2d-dimensional Z-lattices) given by an extension of the work of Sloane (1979) and Conway and Sloane (1988). We show that these constructions produce all of the Niemeier lattices in the case of self-dual codes of length 24, suggesting, by analogy with previous work concerning binary codes, relevance to the classification problem of self-dual conformal field theories in physics. In addition, our intermediate results are of relevance to the classification of self-dual ternary codes of length 24.