论文标题
$δ$ - 可细化的线性代码的分类由重量$Δ$跨越
Classification of $Δ$-divisible linear codes spanned by codewords of weight $Δ$
论文作者
论文摘要
我们对所有$ q $ -ary $δ$ - 可分别的线性代码进行了分类，这些线性代码由重量$Δ$跨越。基本的构建块是单纯码，对于$ q = 2 $，第一阶芦苇毛刺代码和奇偶校验检查代码。这概括了PLESS和SLOANE的结果，该二进制自动执行代码已被分类为$ 4 $的代码，这就是$ Q = 2 $和$δ= 4 $的分类的情况。作为应用程序，我们在投影案例中为二进制$δ$ thenge $4δ$的二进制$δ$可分别代码提供了liu定理的替代证明。
We classify all $q$-ary $Δ$-divisible linear codes which are spanned by codewords of weight $Δ$. The basic building blocks are the simplex codes, and for $q=2$ additionally the first order Reed-Muller codes and the parity check codes. This generalizes a result of Pless and Sloane, where the binary self-orthogonal codes spanned by codewords of weight $4$ have been classified, which is the case $q=2$ and $Δ=4$ of our classification. As an application, we give an alternative proof of a theorem of Liu on binary $Δ$-divisible codes of length $4Δ$ in the projective case.
