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In this paper we show, using a computer-based search exploiting relations of inclusion between arcs and (n,3)-arcs and projective equivalence properties, that the largest size of a complete (n,3)-arc in PG(2,13) is 23 and that only seven non-equivalent (23,3)-arcs exist. From this result, we deduce the non-existence of some [n,k,n-k]13 linear codes and bounds on the minimum distance of some [n,3,d]13...
In this paper the classification of the (n, 3)-arcs in PG(2, 7) is presented. It has been obtained using a computer-based exhaustive search that exploits projective equivalence and produces exactly one representative of each equivalence class. For each (n, 3)-arc, the automorphism group and the maximal size of a contained k-arc have been found.
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