In this paper we show, using a computer-based search exploiting relations of inclusion betweenarcs and (n, 3)-arcs and projective equivalence properties, that the largest size of a complete (n, 3)-arcin PG(2, 13) is 23 and that only seven non-equivalent (23, 3)-arcs exist. From this result, we deducethe non-existence of some [n, k, n−k]13 linear codes and bounds on the minimum distance of some[n, 3, d]13 linear codes. Moreover, we determine the spectrum of the sizes of the complete (n, 3)-arcsin PG(2, 13) and the classification of the smallest complete (n, 3)-arcs.
Maximal (n,3)-arcs in PG(2,13)
MILANI, Alfredo;
2005-01-01
Abstract
In this paper we show, using a computer-based search exploiting relations of inclusion betweenarcs and (n, 3)-arcs and projective equivalence properties, that the largest size of a complete (n, 3)-arcin PG(2, 13) is 23 and that only seven non-equivalent (23, 3)-arcs exist. From this result, we deducethe non-existence of some [n, k, n−k]13 linear codes and bounds on the minimum distance of some[n, 3, d]13 linear codes. Moreover, we determine the spectrum of the sizes of the complete (n, 3)-arcsin PG(2, 13) and the classification of the smallest complete (n, 3)-arcs.File in questo prodotto:
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