Pseudo-Codeword Analysis of Tanner Graphs From Projective and Euclidean Planes

R. Smarandache; P.O. Vontobel

doi:10.1109/tit.2007.899563

Pseudo-Codeword Analysis of Tanner Graphs From Projective and Euclidean Planes

IEEE Transactions on Information Theory ◽

10.1109/tit.2007.899563 ◽

2007 ◽

Vol 53 (7) ◽

pp. 2376-2393 ◽

Cited By ~ 26

Author(s):

R. Smarandache ◽

P.O. Vontobel

Keyword(s):

Euclidean Planes

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Modeling of curls of Agnesi in non-Euclidean planes

10.1063/1.5078477 ◽

2018 ◽

Author(s):

Lyudmila Romakina ◽

Leonid Bessonov ◽

Angelina Chernyshkova

Keyword(s):

Euclidean Planes

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Representations of the Groups of Motions of Euclidean and Pseudo-Euclidean Planes, and Cylindrical Functions

Representation of Lie Groups and Special Functions ◽

10.1007/978-94-011-3538-2_5 ◽

1991 ◽

pp. 165-206

Author(s):

N. Ja. Vilenkin ◽

A. U. Klimyk

Keyword(s):

Euclidean Planes

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An Easy Proof for Some Classical Theorems in Plane Geometry

Canadian Mathematical Bulletin ◽

10.4153/cmb-1992-073-8 ◽

1992 ◽

Vol 35 (4) ◽

pp. 560-568 ◽

Cited By ~ 1

Author(s):

C. Thas

Keyword(s):

Projective Plane ◽

Projective Geometry ◽

The Other ◽

Plane Geometry ◽

The Real ◽

Easy Proof ◽

Special Cases ◽

Euclidean Planes ◽

Straight Lines ◽

Short Method

AbstractThe main result of this paper is a theorem about three conies in the complex or the real complexified projective plane. Is this theorem new? We have never seen it anywhere before. But since the golden age of projective geometry so much has been published about conies that it is unlikely that no one noticed this result. On the other hand, why does it not appear in the literature? Anyway, it seems interesting to "repeat" this property, because several theorems in connection with straight lines and (or) conies in projective, affine or euclidean planes are in fact special cases of this theorem. We give a few classical examples: the theorems of Pappus-Pascal, Desargues, Pascal (or its converse), the Brocard points, the point of Miquel. Finally, we have never seen in the literature a proof of these theorems using the same short method see the proof of the main theorem).

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