Projective Paley sets | Zendy

Cossidente Antonio | Zendy; Marino Giuseppe | Zendy; Pavese Francesco | Zendy

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Projective Paley sets

Author(s) -

Cossidente Antonio,

Marino Giuseppe,

Pavese Francesco

Publication year - 2019

Publication title -

journal of combinatorial designs

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.618

H-Index - 34

eISSN - 1520-6610

pISSN - 1063-8539

DOI - 10.1002/jcd.21666

Subject(s) - hyperplane , quadric , mathematics , combinatorics , automorphism group , invariant (physics) , pencil (optics) , intersection (aeronautics) , projective space , strongly regular graph , projective test , projective plane , set (abstract data type) , character (mathematics) , collineation , automorphism , pure mathematics , geometry , graph , computer science , mechanical engineering , pathwidth , line graph , engineering , mathematical physics , correlation , programming language , aerospace engineering

A two‐character set in PG ( r , q ) is a set X of points with the property that the intersection number with any hyperplane only takes two values. A projective Paley set of PG ( 2 n − 1 , q ) , q odd, is a subset X of points such that every hyperplane of PG ( 2 n − 1 , q ) meets X in either ( q n + 1 ) ( q n − 1 − 1 ) ∕ 2 ( q − 1 ) or ( q n − 1 ) ( q n − 1 + 1 ) ∕ 2 ( q − 1 ) points. A quasi‐quadric in PG ( 2 n − 1 , q ) is a two‐character set that has the same size and the same intersection numbers with respect to hyperplanes as a nondegenerate quadric. Here we construct projective Paley sets of PG ( 3 , q ) left invariant by a cyclic group of order q 2 + 1 and of PG ( 5 , q ) admitting PSL ( 2 , q 2 ) as an automorphism group. Also infinite families of quasi‐quadrics of PG ( 5 , q ) are provided.

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