Computational Enumeration of André Planes

2021/05/16 by Jeremy M. Dover, Dover, Jeremy M.
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.CO

paper · pdf · doi:10.48550/arxiv.2105.07439

arxiv created 2021/05/16 · openalex publication_date 2021/05/16 · arxiv updated 2021/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we address computational questions surrounding the enumeration of non-isomorphic André planes for any prime power order. We are particularly focused on providing a complete enumeration of all such planes for relatively small orders (up to 125), as well as developing computationally efficient ways to count the number of isomorphism classes for other orders where enumeration is infeasible. André planes of all dimensions over their kernel are considered.

Citations

• A genealogy of the translation planes of order 25

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