Suppose \(q=2^h\) to be an even prime power. Then there exist \([q+2,3,q]\) MDS codes and these codes correspond to the projective system of the points of a hyperoval in the finite projective plane \(\mathrm{PG}(2,q)\). In the paper under review, extended cyclic codes arising from a construction of C. Ding [Designs from linear codes. Hackensack, NJ: World Scientific (2019; Zbl 1408.94003)] are considered and the question of which hyperovals might be obtained in that way is addressed. In particular, the authors first show that extended cyclic codes with parameters \([q+2,3,q]\) are equivalent to codes arising from regular hyperovals. Next, they extend their result to show that \([qt-q+t,3,qt-q]\) extended cyclic codes (with \(1<t<q\)) where \(q\) is a power of \(t\) correspond to cyclic Denniston maximal arcs. Finally, these results are extended to MDS codes of dimension \(4\), by proving that a cyclic code over \({\mathbb F}_q\) of parameters \([q^2+1,4,q^2 -q]\) is equivalent to an ovoid code obtained from an elliptic quadric in \(\mathrm{PG}(3,q)\).