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Designs, Codes and Cryptography
Published in: Designs, Codes and Cryptography 8/2019

19-11-2018

Cameron–Liebler sets of k-spaces in \({{\mathrm{PG}}}(n,q)\)

Authors: A. Blokhuis, M. De Boeck, J. D’haeseleer

Published in: Designs, Codes and Cryptography | Issue 8/2019

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Abstract

Cameron–Liebler sets of k-spaces were introduced recently in Filmus and Ihringer (J Combin Theory Ser A, 2019). We list several equivalent definitions for these Cameron–Liebler sets, by making a generalization of known results about Cameron–Liebler line sets in \({{\mathrm{PG}}}(n,q)\) and Cameron–Liebler sets of k-spaces in \({{\mathrm{PG}}}(2k+1,q)\). We also present some classification results.
previous article Optimal binary constant weight codes and affine linear groups over finite fields
next article Additive perfect codes in Doob graphs
Literature
1.
Blokhuis A., Brouwer A.E., Chowdhury A., Frankl P., Mussche T., Patkós B., Szőnyi T.: A Hilton-Milner theorem for vector spaces. Electron. J. Comb. 17, 71 (2010).MathSciNetCrossRef
2.
Brouwer A.E., Cohen A.M., Neumaier A.: Distance-Regular Graphs. Springer, Berlin (1989).CrossRef
3.
Brouwer A.E., Cioabǎ S.M., Ihringer F., McGinnis M.: The smallest eigenvalues of Hamming graphs, Johnson graphs and other distance-regular graphs with classical parameters. arXiv:​1709.​09011 (2017).
4.
Bruen A.A., Drudge K.: The construction of Cameron-Liebler line classes in \(\text{ PG }(3, q)\). Finite Fields Appl. 5(1), 35–45 (1999).MathSciNetCrossRef
5.
Cameron P.J., Liebler R.A.: Tactical decompositions and orbits of projective groups. Linear Algebra Appl. 46, 91–102 (1982).MathSciNetCrossRef
6.
7.
De Beule J., Demeyer J., Metsch K., Rodgers M.: A new family of tight sets in \(Q^+(5, q)\). Des. Codes Cryptogr. 78(3), 655–678 (2016).MathSciNetCrossRef
8.
9.
De Boeck M., Rodgers M., Storme L., Švob A.: Cameron-Liebler sets of generators in finite classical polar spaces. arXiv:​1712.​06176 (submitted) (2017).
10.
Drudge K.: Extremal sets in projective and polar spaces. PhD thesis, University of Western Ontario (1998).
11.
Eisfeld J.: The eigenspaces of the Bose-Mesner algebras of the association schemes corresponding to projective spaces and polar spaces. Des. Codes Cryptogr. 17, 129–150 (1999).MathSciNetCrossRef
12.
Feng T., Momihara K., Xiang Q.: Cameron-Liebler line classes with parameter \(x=\frac{q^2-1}{2}\). J. Comb. Theory A 133, 307–338 (2015).CrossRef
13.
Filmus Y., Ihringer F.: Boolean degree 1 functions on some classical association schemes. J. Combin. Theory Ser. A (2019).
14.
15.
16.
Gavrilyuk A.L., Metsch K.: A modular equality for Cameron-Liebler line classes. J. Comb. Theory A 127, 224–242 (2014).MathSciNetCrossRef
17.
18.
Gavrilyuk A.L., Mogilnykh I.Y.: Cameron-Liebler line classes in \(\text{ PG }(n,4)\). Des. Codes Cryptogr. 73(3), 969–982 (2014).MathSciNetCrossRef
19.
Godsil C., Meagher K.: Erdös-Ko-Rado Theorems: Algebraic Approaches. Cambridge Studies in Advanced Mathematics, vol. 149. Cambridge University Press, Cambridge (2016).MATH
20.
21.
Metsch K.: The non-existence of Cameron-Liebler line classes with parameter \(2<x<q\). Bull. Lond. Math. Soc. 42(6), 991–996 (2010).MathSciNetCrossRef
22.
Metsch K.: An improved bound on the existence of Cameron-Liebler line classes. J. Comb. Theory A 121, 89–93 (2014).MathSciNetCrossRef
23.
24.
Newman M.: Independent sets and eigenspaces. PhD thesis, University of Waterloo (2004).
25.
26.
27.
Segre B.: Lectures on Modern Geometry (with an appendix by L. Lombardo-Radice). Consiglio Nazionale delle Ricerche, Monografie Mathematiche. Edizioni Cremonese, Roma, 479 pp. (1961).
28.
Segre B.: Teoria di Galois, fibrazioni proiettive e geometrie non desarguesiane. Ann. Mat. Pura Appl. 64(4), 1–76 (1964).MathSciNetCrossRef
Metadata
Title
Cameron–Liebler sets of k-spaces in
Authors
A. Blokhuis
M. De Boeck
J. D’haeseleer
Publication date
19-11-2018
Publisher
Springer US
Published in
Designs, Codes and Cryptography / Issue 8/2019
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-018-0583-1

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