论文标题
二进制线性代码的偏置置换自动形态
Involutory permutation automorphisms of binary linear codes
论文作者
论文摘要
我们研究了均匀长度的二进制线性代码的性能，其置换自动形态群是由互动产生的环状组。为了达到尺寸或共同含量$ 4 $，我们表明没有准组代码的置换自动形态组是同构为$ C_2 $。通过概括该方法来证明这一结果，我们可以获得假定的极端自动划分$ [72、36、16] $和$ [96、48、20] $代码的结果。
We investigate the properties of binary linear codes of even length whose permutation automorphism group is a cyclic group generated by an involution. Up to dimension or co-dimension $4$, we show that there is no quasi group code whose permutation automorphism group is isomorphic to $C_2$. By generalizing the method we use to prove this result, we obtain results on the structure of putative extremal self-dual $[72, 36, 16]$ and $[96, 48, 20]$ codes in the presence of an involutory permutation automorphism.
