Complete (k, 4)-arcs in projective Galois planes are the geometric counterpart of linear non-extendible codes of length k, dimension 3 and Singleton defect 2. A class of infinite families of complete (k, 4)-arcs in PG(2, q) is constructed, for q a power of an odd prime p equivalent to 3 (mod 4), p > 3. The order of magnitude of k is smaller than q. This property significantly distinguishes the complete (k, 4)-arcs of this paper from the previously known infinite families, whose size exceeds q - 6 root q.

Complete (k, 4)-arcs from quintic curves

Bartoli, D;
2017

Abstract

Complete (k, 4)-arcs in projective Galois planes are the geometric counterpart of linear non-extendible codes of length k, dimension 3 and Singleton defect 2. A class of infinite families of complete (k, 4)-arcs in PG(2, q) is constructed, for q a power of an odd prime p equivalent to 3 (mod 4), p > 3. The order of magnitude of k is smaller than q. This property significantly distinguishes the complete (k, 4)-arcs of this paper from the previously known infinite families, whose size exceeds q - 6 root q.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1534993
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