The Spectrum of Values k for Complete \(k\)-Arcs in PG\((2,q)\) for \(q \leq 23\)

Arcs and linear maximum distance separable \((M.D.S.)\) codes are equivalent objects~\([25]\). Hence, all results on arcs can be expressed in terms of linear M.D.S. codes and conversely. The list of all complete \(k\)-arcs in \(\mathrm{PG}(2,q)\) has been previously determined for \(q \leq 16\). In this paper, (i) all values of \(k\) for which there exists a complete \(k\)-arc in \(\mathrm{PG}(2,q)\), with \(17 \leq q \leq 23\), are determined; (ii) a complete \(k\)-arc for each such possible \(k\) is exhibited.