TY - JOUR
AU1 - Barwick, S.
AU2 - Hui, Alice
AU3 - Jackson, Wen-Ai
AU4 - Schillewaert, Jeroen
AB - Let 
$${\mathcal {H}}$$


H


 be a non-empty set of hyperplanes in 
$$\text {PG}(4,q)$$



PG
(
4
,
q
)



, q even, such that every point of 
$$\text {PG}(4,q)$$



PG
(
4
,
q
)



 lies in either 0, 
$$\frac{1}{2}q^3$$




1
2


q
3




 or 
$$\frac{1}{2}(q^3+q^2)$$




1
2


(

q
3

+

q
2

)




 hyperplanes of 
$${\mathcal {H}}$$


H


, and every plane of 
$$\text {PG}(4,q)$$



PG
(
4
,
q
)



 lies in 0 or at least 
$$\frac{1}{2}q$$




1
2

q



 hyperplanes of 
$${\mathcal {H}}$$


H


.  Then 
$${\mathcal {H}}$$


H


 is the set of all hyperplanes which meet a given non-singular quadric Q(4, q) in a hyperbolic quadric.
TI - Characterising hyperbolic hyperplanes of a non-singular quadric in $$\text {PG}(4,q)$$ PG ( 4 , q )
JF - Designs, Codes and Cryptography
DO - 10.1007/s10623-019-00669-y
DA - 2019-08-01
UR - https://www.deepdyve.com/lp/springer-journals/characterising-hyperbolic-hyperplanes-of-a-non-singular-quadric-in-X5ZoOOSvU0
SP - 33
EP - 39
VL - 88
IS - 1
DP - DeepDyve
ER -