论文标题
在二进制线性恒定重量代码及其自构群上
On the binary linear constant weight codes and their autormorphism groups
论文作者
论文摘要
我们通过使用代码字支持的对称差异给二进制线性恒定重量代码的表征。这种表征给出了二进制线性恒定重量代码集与代码字支持联合的分区集之间的对应关系。通过使用此通信，我们为二进制线性恒定重量代码的自动形态组的顺序提出了一个公式，就其参数而言。该公式是用给定参数确定恒定重量代码上更多代数结构的关键步骤。 Bonisoli [Bonisoli，A。：每个等距线性代码都是双重锤代码的序列。 Ars Combinatoria 18, 181--186 (1984)] proves that the $q$-ary linear constant weight codes with the same parameters are equivalent (for the binary case permutation equivalent).我们还通过在代码字支持的对称差异上呈现明确的置换，为Bonisoli定理提供了替代证明，该置换量在二进制线性恒定重量代码之间列出了置换等效性。
We give a characterization for the binary linear constant weight codes by using the symmetric difference of the supports of the codewords. This characterization gives a correspondence between the set of binary linear constant weight codes and the set of partitions for the union of supports of the codewords. By using this correspondence, we present a formula for the order of the automorphism group of a binary linear constant weight code in terms of its parameters. This formula is a key step to determine more algebraic structures on constant weight codes with given parameters. Bonisoli [Bonisoli, A.: Every equidistant linear code is a sequence of dual Hamming codes. Ars Combinatoria 18, 181--186 (1984)] proves that the $q$-ary linear constant weight codes with the same parameters are equivalent (for the binary case permutation equivalent). We also give an alternative proof for Bonisoli's theorem by presenting an explicit permutation on symmetric difference of the supports of the codewords which gives the permutation equivalence between the binary linear constant weight codes.
