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Designs, Codes and Cryptography

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09-02-2017

Derivation of Cameron–Liebler line classes

Authors: Alexander L. Gavrilyuk, Ilia Matkin, Tim Penttila

Published in: Designs, Codes and Cryptography | Issue 1/2018

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Abstract

We construct a new infinite family of Cameron–Liebler line classes in \(\textsc {PG}(3,q)\) with parameter \(x=\frac{q^2+1}{2}\) for all odd q.

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Bruen A.A., Drudge K.: The construction of Cameron–Liebler line classes in PG(3, \(q)\). Finite Fields Appl. 5(1), 35–45 (1999).MathSciNetCrossRefMATH

Cameron P.J., Liebler R.A.: Tactical decompositions and orbits of projective groups. Linear Algebra Appl. 46, 91–102 (1982).MathSciNetCrossRefMATH

Cossidente A., Pavese F.: Intriguing sets of quadrics in PG(5, \(q)\). Adv. Geom. (in press).

De Beule J., Demeyer J., Metsch K., Rodgers M.: A new family of tight sets in \(Q^+(5, q)\). Des. Codes Cryptogr. 78, 655–678 (2016).MathSciNetCrossRefMATH

Drudge K.: Extremal sets in projective and polar spaces. Ph.D. Thesis, University of Western Ontario (1998).

Drudge K.: On a conjecture of Cameron and Liebler. Eur. J. Comb. 20(4), 263–269 (1999).MathSciNetCrossRefMATH

Feng T., Momihara K., Xiang Q.: Cameron–Liebler line classes with parameter \(x=\frac{q^2-1}{2}\). J. Comb. Theory Ser. A 133, 307–338 (2015).MathSciNetCrossRefMATH

Gavrilyuk A.L., Metsch K.: A modular equality for Cameron–Lieber line classes. J. Comb. Theory Ser. A 127, 224–242 (2014).CrossRefMATH

Gavrilyuk A.L., Mogilnykh I.Y.: Cameron–Liebler line classes in \({\rm PG}(n,4)\). Des. Codes Cryptogr. 73(3), 969–982 (2014).MathSciNetCrossRefMATH

10.

Govaerts P., Penttila T.: Cameron–Liebler line classes in \({\rm PG}(3,4)\). Bull. Belg. Math. Soc. Simon Stevin 12(5), 793–804 (2005).MathSciNetMATH

11.

Metsch K.: An improved bound on the existence of Cameron–Liebler line classes. J. Comb. Theory Ser. A 121, 89–93 (2014).MathSciNetCrossRefMATH

12.

Penttila T.: Cameron–Liebler line classes in \({\rm PG}(3, q)\). Geom. Dedicata 37(3), 245–252 (1991).MathSciNetCrossRefMATH

13.

Qvist B.: Some remarks concerning curves of the second degree in a finite plane. Suomalainen tiedeakatemia (Sci. Fenn.) 134, 4–27 (1952).MathSciNetMATH

14.

Rodgers M.: Cameron–Liebler line classes. Des. Codes Cryptogr. 68(1–3), 33–37 (2013).MathSciNetCrossRefMATH

15.

Segre B.: Ovals in a finite projective plane. Can. J. Math. 7, 414–416 (1955).MathSciNetCrossRefMATH

Title: Derivation of Cameron–Liebler line classes
Authors: Alexander L. Gavrilyuk
Ilia Matkin
Tim Penttila
Publication date: 09-02-2017
Publisher: Springer US
Published in: Designs, Codes and Cryptography / Issue 1/2018
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI: https://doi.org/10.1007/s10623-017-0338-4

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