Geodesic
Cyclic arcs in $PG(2,q)$
Journal of Algebraic Combinatorics, Tome 3 (1994) no. 1, pp. 113-128.

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Summary: B.C. Kestenband [9], J.C. Fisher, J.W.P. Hirschfeld, and J.A. Thas [3], E. Boros, and T. Szönyi [1] constructed complete $( q ^{2} - q + l)$-arcs in $P$G$(2, q ^{2}), qge$ 3. One of the interesting properties of these arcs is the fact that they are fixed by a cyclic protective group of order $q ^{2} - q + 1$. We investigate the following problem: What are the complete $k$-arcs in $P$G$(2, q)$ which are fixed by a cyclic projective group of order $k$? This article shows that there are essentially three types of those arcs, one of which is the conic in $P$G$(2, q), q$ odd. For the other two types, concrete examples are given which shows that these types also occur.
Keywords: $k$-arc, conic, M.D.S. code, cyclic group 
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     author = {Storme, L. and Van Maldeghem, H.},
     title = {Cyclic arcs in $PG(2,q)$},
     journal = {Journal of Algebraic Combinatorics},
     pages = {113--128},
     publisher = {mathdoc},
     volume = {3},
     number = {1},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_1994__3_1_a0/}
}
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Storme, L.; Van Maldeghem, H. Cyclic arcs in $PG(2,q)$. Journal of Algebraic Combinatorics, Tome 3 (1994) no. 1, pp. 113-128. http://geodesic.mathdoc.fr/item/JAC_1994__3_1_a0/