Complete (k,3)-arcs in projective planes over finite fields are the geometric counterpart of linear non-extendible Near MDS codes of length k and dimension 3. A class of infinite families of complete (k,3)-arcs in PG(2,q) is constructed, for q a power of an odd prime p≡2(mod3). The order of magnitude of k is smaller than q. This property significantly distinguishes the complete (k,3)-arcs of this paper from the previously known infinite families, whose size differs from q by at most 2q√.

Complete (k ,3) -arcs from quartic curves

BARTOLI, DANIELE;GIULIETTI, Massimo;
2015-01-01

Abstract

Complete (k,3)-arcs in projective planes over finite fields are the geometric counterpart of linear non-extendible Near MDS codes of length k and dimension 3. A class of infinite families of complete (k,3)-arcs in PG(2,q) is constructed, for q a power of an odd prime p≡2(mod3). The order of magnitude of k is smaller than q. This property significantly distinguishes the complete (k,3)-arcs of this paper from the previously known infinite families, whose size differs from q by at most 2q√.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1344513
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