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Modular Descriptions of Regular Functions Read chapter Read first chapter

2019 | OriginalPaper | Chapter

Parallelisms of \(\mathrm{PG}(3,4)\) Invariant Under Cyclic Groups of Order 4

Authors : Anton Betten, Svetlana Topalova, Stela Zhelezova

Published in: Algebraic Informatics

Publisher: Springer International Publishing

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Abstract

A spread in \(\mathrm{PG}(n,q)\) is a set of mutually skew lines which partition the point set. A parallelism is a partition of the set of lines by spreads. The classification of parallelisms in small finite projective spaces is of interest for problems from projective geometry, design theory, network coding, error-correcting codes, cryptography, etc. All parallelisms of \(\mathrm{PG}(3,2)\) and \(\mathrm{PG}(3,3)\) are known and parallelisms of \(\mathrm{PG}(3,4)\) which are invariant under automorphisms of odd prime orders and under the Baer involution have already been classified. In the present paper, we classify all (we establish that their number is 252738) parallelisms in \(\mathrm{PG}(3,4)\) that are invariant under cyclic automorphism groups of order 4. We compute the order of their automorphism groups and obtain invariants based on the type of their spreads and duality.

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previous chapter Maximal Diameter on a Class of Circulant Graphs
next chapter Bounds on Covering Codes in RT Spaces Using Ordered Covering Arrays
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Metadata
Title
Parallelisms of Invariant Under Cyclic Groups of Order 4
Authors
Anton Betten
Svetlana Topalova
Stela Zhelezova
Copyright Year
2019
Book
Algebraic Informatics

Print ISBN: 978-3-030-21362-6

Electronic ISBN: 978-3-030-21363-3

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-21363-3_8

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