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COORDINATISING PLANES OF PRIME POWER ORDER USING FINITE FIELDS

Part of: Designs and configurations General field theory Finite geometry and special incidence structures

Published online by Cambridge University Press:  22 August 2018

ROBERT S. COULTER Open the ORCID record for ROBERT S. COULTER [Opens in a new window]
ROBERT S. COULTER*
Affiliation:
520 Ewing Hall, Department of Mathematical Sciences, University of Delaware, Newark, DE19716, USA email coulter@udel.edu
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Abstract

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We revisit the coordinatisation method for projective planes by considering the consequences of using finite fields to coordinatise projective planes of prime power order. This leads to some general restrictions on the form of the resulting planar ternary ring (PTR) when viewed as a trivariate polynomial over the field. We also consider how the Lenz–Barlotti type of the plane being coordinatised impacts the form of the PTR polynomial, thereby deriving further restrictions.

Keywords

projective planespolynomials over finite fieldsplanar ternary ringscoordinatisation method

MSC classification

Primary: 51E15: Affine and projective planes
Secondary: 12E05: Polynomials (irreducibility, etc.) 05B25: Finite geometries
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 106 , Issue 2 , April 2019 , pp. 184 - 199
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

The results of this article were presented as part of a plenary talk given at the National Conference on Coding Theory and Cryptography 2017 (1–4 September), in Hangzhou, China.

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