image-caps of class image and type image of PG(5, image) are quadric Veroneseans

The quadric Veronesean View the MathML sourceV24 in PG(5,q)(5,q) is characterized as a (q2+q+1)(q2+q+1)-cap of class [0,1,2,3,q+1]2[0,1,2,3,q+1]2 and type (1,q+1,2q+1)4(1,q+1,2q+1)4 of PG(5,q)(5,q) by Ferri (q odd) and Thas and Van Maldeghem (q even). In this note we generalize this result slightly by proving that for a (q2+q+1)(q2+q+1)-cap of class [0,1,2,3,q+1]2[0,1,2,3,q+1]2 and type (1,m,n)4(1,m,n)4 of PG(5,q)(5,q), the parameters m and n are uniquely determined and equal q+1q+1 and 2q+12q+1, respectively.