一类具有最小阴影的单偶self-dual码的不存在性
Nonexistence of certain singly even self-dual codes with minimal shadow
摘要：
已知对于$(n,d)=(24m+2,4m+4)$、$(24m+4,4m+4)$、$(24m+6,4m+4)$、$(24m+10,4m+4)$和$(24m+22,4m+6)$不存在具有最小阴影的极值单偶自对偶$[n,n/2,d]$码。本文研究了具有最小阴影的单偶自对偶码的最小权$d-2$。对于$n=24m+2$，$24m+4$和$24m+10$，我们证明了具有最小阴影的单偶自对偶$[n,n/2,4m+2]$码的权枚举数是唯一确定的，并且证明了对于$m \ge 155$，$m \ge 156$和$m \ge 160$，不存在具有最小阴影的单偶自对偶$[n,n/2,4m+2]$码.我们证明了具有最小阴影的单偶自对偶码的重量枚举数对于参数$[24m+6,12m+3,4m+2]$和$[24m+22,12m+11,4m+4]$不是唯一确定的。
英文摘要：
It is known that there is no extremal singly even self-dual $[n,n/2,d]$ code with minimal shadow for $(n,d)=(24m+2,4m+4)$, $(24m+4,4m+4)$, $(24m+6,4m+4)$, $(24m+10,4m+4)$ and $(24m+22,4m+6)$. In this paper, we study singly even self-dual codes with minimal shadow having minimum weight $d-2$ for these $(n,d)$. For $n=24m+2$, $24m+4$ and $24m+10$, we show that the weight enumerator of a singly even self-dual $[n,n/2,4m+2]$ code with minimal shadow is uniquely determined and we also show that there is no singly even self-dual $[n,n/2,4m+2]$ code with minimal shadow for $m \ge 155$, $m \ge 156$ and $m \ge 160$, respectively. We demonstrate that the weight enumerator of a singly even self-dual code with minimal shadow is not uniquely determined for parameters $[24m+6,12m+3,4m+2]$ and $[24m+22,12m+11,4m+4]$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
