Classification of (0,2)-geometries embedded in AG (3,q)

In De Clerck and Delanote (Des. Codes Cryptogr, 32: 103–110, 2004) it is shown that if a (0,α)-geometry with α ≥  3 is fully embedded in AG (n,q) then it is a linear representation. In De Feyter (J. Combin Theory Ser A, 109(1): 1–23, 2005; Discrete math, 292: 45–54, 2005) the (0,2)-geometries fully embedded in AG(3,q) are classified apart from two open cases. In this paper, we solve these two open cases. This classification for AG(3,q) is used in De Feyter (Adv Geom, 5: 279–292, 2005) to classify the (0,2)-geometries fully embedded in AG(n,q).