Advances and Applications in Discrete Mathematics

The Advances and Applications in Discrete Mathematics is a prestigious peer-reviewed journal indexed in the Emerging Sources Citation Index (ESCI). It is dedicated to publishing original research articles in the field of discrete mathematics and combinatorics, including topics such as graphs, coding theory, and block design. The journal emphasizes efficient and powerful tools for real-world applications and welcomes expository articles that highlight current developments in the field.

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A CONSTRUCTION OF FINITE PROJECTIVE PLANES

Authors

  • Norichika Matsuki

Keywords:

finite projective plane, incidence matrix, sequence

DOI:

https://doi.org/10.17654/0974165826010

Abstract

We propose a new method to construct a finite projective plane. Its incidence matrix is expressed in the special Paige-Wexler normal form whose lower right part is a circulant block matrix.

Received: December 3, 2025
Accepted: December 30, 2025

References

[1] C. Balbuena, Incidence matrices of projective planes and of some regular bipartite graphs of girth 6 with few vertices, SIAM J. Discrete Math. 22 (2008), 1351-1363.

[2] D. Crnković, V. M. Crnković, F. Pavese and A. Švob, Construction of the projective plane from the unitary group Contrib. Discrete Math. 19 (2024), 178-183.

[3] P. Dembowski, Finite Geometries, Springer-Verlag, Berlin, 1968.

[4] M. Hall, Projective planes, Trans. Amer. Math. Soc. 54 (1943), 229-277.

[5] A. D. Keedwell and J. Dénes, Latin Squares and Their Applications, 2nd ed., North-Holland, Amsterdam, 2015.

[6] C. W. H. Lam, L. Thiel and S. Swiercz, The non-existence of finite projective planes of order 10, Canad. J. Math. 41 (1989), 1117-1123.

[7] L. J. Paige and C. Wexler, A canonical form for incidence matrices of finite projective planes and their associated Latin squares, Port. Math. 12 (1953), 105 112.

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Published

2026-01-03

Issue

Vol. 43 No. 2 (2026)

Section

Articles

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How to Cite

A CONSTRUCTION OF FINITE PROJECTIVE PLANES. (2026). Advances and Applications in Discrete Mathematics, 43(2), 147-154. https://doi.org/10.17654/0974165826010

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