2-Ranks of incidence matrices associated with conics in finite projective planes

Megan Adams; Junhua Wu

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2-Ranks of incidence matrices associated with conics in finite projective planes

机译：有限投影平面中与圆锥相关的入射矩阵的2级

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In this article, we investigate geometric properties of the secant-internal neighbors of internal points and the passant-external neighbors of external points in classical finite projective planes; we calculate the 2-ranks of the incidence matrices of internal points versus their secant-internal neighbors and external points versus their passant-external neighbors using a combination of techniques from both finite geometry and linear algebra.

机译：在本文中，我们研究了经典有限射影平面中内部点的割线-内部邻居和外部点的通过线-外部邻居的几何性质；我们使用有限几何和线性代数的技术组合，计算了内部点与它们的割线-内部邻居，外部点与它们的传递-外部邻居的发生矩阵的2级。

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来源
《Designs, Codes and Crytography》 |2014年第2期|381-404|共24页
作者
Megan Adams; Junhua Wu;
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作者单位

Department of Mathematics, Lane College, Jackson, TN, USA;

Department of Mathematics, Lane College, Jackson, TN, USA;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Conic; Incidence matrix; Low-density parity-check code; Module; 2-Rank;

机译：锥;发病率矩阵;低密度奇偶校验码;模块;2排;

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专利

1. Conics and orthogonal projectivities in a finite plane [J] . W. L. Edge Canadian Journal of Mathematics . 1956,第1956期

机译：有限平面中的圆锥和正交投影
2. INCIDENCE MATRICES OF PROJECTIVE PLANES AND OF SOME REGULAR BIPARTITE GRAPHS OF GIRTH 6 WITH FEW VERTICES [J] . C. BALBUENA SIAM Journal on Discrete Mathematics . 2008,第4期

机译：几个平面的射影平面和一些周长为6的规则双方图的入射矩阵
3. On the rank of incidence matrices for points and lines of finite affine and projective geometries over a field of four elements [J] . Jan De Beule Computing reviews . 2015,第4期

机译：关于四元素场上有限仿射和投影几何的点和线的入射矩阵的秩
4. Representation of conics in the oriented projective plane [C] . Pinto, G.A., De Rezende, . 1997

机译：圆锥投影在定向投影平面中的表示
5. Geometric structures and linear codes related to conics in classical projective planes of odd orders. [D] . Wu, Junhua. 2008

机译：与奇数阶经典投影平面中的圆锥曲线有关的几何结构和线性代码。
6. Projecting contact matrices in 177 geographical regions: An update and comparison with empirical data for the COVID-19 era [O] . Kiesha Prem, Kevin van Zandvoort, Petra Klepac, 2021

机译：在177个地理区域预测矩阵：与Covid-19时代的经验数据更新和比较
7. Incidence Matrices of Finite Projective Planes and Their Eigenvalues [O] . Department of Mathematics, University of Florida, Gainesville, Florida, 32611 ( host institution ), Thompson, John G. ( UF author ) 1997

机译：有限射影平面的入射矩阵及其特征值
8. Plane Wave (EMP) Incidence on a Finitely Conducting Plane Earth with the Magnetic Field Intensity Parallel to the Earth's Surface [R] . Neff, H. P., Reed, D. A. 1984

机译：平面波（Emp）在有限导电平面地球上的入射，其磁场强度平行于地球表面

2-Ranks of incidence matrices associated with conics in finite projective planes

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