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Designs, Codes and Cryptography
Published in: Designs, Codes and Cryptography 6/2021

06-04-2021

Cameron–Liebler sets in bilinear forms graphs

Author: Jun Guo

Published in: Designs, Codes and Cryptography | Issue 6/2021

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Abstract

Cameron–Liebler sets of subspaces in projective spaces were studied recently by Blokhuis et al. (Des Codes Cryptogr 87:1839–1856, 2019). In this paper, we discuss Cameron–Liebler sets in bilinear forms graphs, obtain several equivalent definitions and present some classification results.
previous article Flag-transitive 4-designs and PSL(2, q) groups
next article Differential spectra of a class of power permutations with characteristic 5
Footnotes
1
For each \((x_1,\ldots ,x_{n})^t\in \mathbb {F}_q^{n}\), let \(V_{(x_1,\ldots ,x_{n})}=\langle e_1+x_1e_{n+1},\ldots ,e_n+x_ne_{n+1},e_{n+2},\ldots ,e_{n+\ell }\rangle .\) Then \(\{V_{(x_1,\ldots ,x_{n})}: (x_1,\ldots ,x_{n})^t\in \mathbb {F}_q^{n}\}\subseteq {\mathcal {M}}(n+\ell -1,\ell -1;n+\ell ,E)\) and \({\mathcal {M}}_n(V_{(x_1,\ldots ,x_{n})})\cap {\mathcal {M}}_n(V_{(y_1,\ldots ,y_{n})})=\emptyset \) for all \((x_1,\ldots ,x_{n})\not =(y_1,\ldots ,y_{n})\).
 
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Metadata
Title
Cameron–Liebler sets in bilinear forms graphs
Author
Jun Guo
Publication date
06-04-2021
Publisher
Springer US
Published in
Designs, Codes and Cryptography / Issue 6/2021
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-021-00864-w

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