The Subschemes of the Hamming Scheme
The Subschemes of the Hamming Scheme
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汉明方案的子方案
DOI：
10.1007/978-94-017-1972-8_4
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
M. E. Muzichuk
中科院分区：
文献类型：
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作者：
M. E. Muzichuk
本文包含锤子方案h的所有亚物种的完整表征（n，2）。组\（{s _ {{2^n}}} \）。二在[4]中，n≤16的所有n的分类都可以通过计算机分类。我们的概念是，当n足够大时，该概念的数量变得稳定。
The present paper contains the complete characterization of all the subschemes of the Hamming scheme H(n, 2). The characterization problem for these subschemes is closely related to the study of the lattice of overgroups of the exponentiation S 2 ↑ S n in the symmetric group \({S_{{2^n}}}\). For this reason the results of the paper can be used in the study of symmetry in algebraic code s, and in the classification of Boolean functions. Some examples of subschemes having two classes for even n were indicated in [4]. All subschemes of H(n, 2) for n ≤ 16 have been classified by computer. A synopsis of these results on enumeration can be found in [5]. An analysis of them led us to a conjecture that the number of subschemes becomes stable when n is sufficiently large. The validity of this conjecture follows from the list of the subschemes of H(n, 2) presented below.