论文标题
最大弧，代码和投影平面之间的新链接
Maximal arcs, codes, and new links between projective planes
论文作者
论文摘要
在本文中，我们考虑了二进制线性代码，该二进制线性代码是由Steiner 2设计与最大弧相关的偶数均匀平面及其双重代码相关的最大弧相关的发病率矩阵。衍生出2级矩阵上的上限和下边界。证明了双重代码最小距离的下限，并且仅当相关最大弧含有平面的高卵形时，才能达到结合。长度为52的二进制线性代码，由2- $（52,4,1）$设计与先前已知的和一些新发现的第4级最大弧相关的发射率矩阵跨度16中的最大弧线进行分析，并分类为等效性。该分类表明，非同构平面中与最大弧相关的某些设计会生成等效的代码。这种现象在几个已知平面之间建立了新的联系。制定了有关$ pg（2,2^m）$中最大弧代码的猜想。
In this paper we consider binary linear codes spanned by incidence matrices of Steiner 2-designs associated with maximal arcs in projective planes of even order, and their dual codes. Upper and lower bounds on the 2-rank of the incidence matrices are derived. A lower bound on the minimum distance of the dual codes is proved, and it is shown that the bound is achieved if and only if the related maximal arc contains a hyperoval of the plane. The binary linear codes of length 52 spanned by the incidence matrices of 2-$(52,4,1)$ designs associated with previously known and some newly found maximal arcs of degree 4 in projective planes of order 16 are analyzed and classified up to equivalence. The classification shows that some designs associated with maximal arcs in nonisomorphic planes generate equivalent codes. This phenomenon establishes new links between several of the known planes. A conjecture concerning the codes of maximal arcs in $PG(2,2^m)$ is formulated.
