关于F^n到二元汉明码的传递一致分拆
On transitive uniform partitions of F^n into binary Hamming codes
摘要：
本文研究了Galois域$GF(2)$上维数为$n$的向量空间$F^n$到汉明码陪集的传递性均匀划分.将$F^n$划分为长度为$n$的汉明码$H_0,H_1,\ldots,H_n$的陪集的划分$P^n= \{H_0,H_1+e_1,\ldots,H_n+e_n\}$被称为是均匀的，如果任何两个码$H_i$和$H_j$的交集，$i,j\in \{0,1,\ldots,n \}$是常数，这里$e_i$是权重为$1$的$F^n$中的二进制向量，在第$i$个坐标位置中为1。对任意的$n=2^m-1$，$m>4$，我们找到了一类非等价的$2$ -传递均匀分拆，把$F^n$划分为Hamming码的陪集.
英文摘要：
We investigate transitive uniform partitions of the vector space $F^n$ of dimension $n$ over the Galois field $GF(2)$ into cosets of Hamming codes. A partition $P^n= \{H_0,H_1+e_1,\ldots,H_n+e_n\}$ of $F^n$ into cosets of Hamming codes $H_0,H_1,\ldots,H_n$ of length $n$ is said to be uniform if the intersection of any two codes $H_i$ and $H_j$, $i,j\in \{0,1,\ldots,n \}$ is constant, here $e_i$ is a binary vector in $F^n$ of weight $1$ with one in the $i$th coordinate position. For any $n=2^m-1$, $m>4$ we found a class of nonequivalent $2$-transitive uniform partitions of $F^n$ into cosets of Hamming codes.
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