We point out an interplay between F-q,-Frobenius non-classical plane curves and complete (k, d)-arcs in P-2( F-q). A typical example that shows how this works is the one concerning an Hermitian curve. We present some other examples here which give rise to the existence of new complete (k, d)-arcs with parameters k = d(q - d + 2) and d = (q - 1)/(q' - 1), q' being a power of the characteristic. In addition, for q a square, new complete (k, d)-arcs with either k = qrootqb + 1 and d = (rootq + 1)b(2 less than or equal to b less than or equal to rootq - 1) or k = (q - 1)\rootqb + rootq + 1 and d = (rootq +1)b(2 less than or equal to b less than or equal to rootq - 2) are constructed by using certain reducible plane curves.
On complete arcs arising from plane curves
GIULIETTI, Massimo;PAMBIANCO, Fernanda;UGHI, Emanuela
2002
Abstract
We point out an interplay between F-q,-Frobenius non-classical plane curves and complete (k, d)-arcs in P-2( F-q). A typical example that shows how this works is the one concerning an Hermitian curve. We present some other examples here which give rise to the existence of new complete (k, d)-arcs with parameters k = d(q - d + 2) and d = (q - 1)/(q' - 1), q' being a power of the characteristic. In addition, for q a square, new complete (k, d)-arcs with either k = qrootqb + 1 and d = (rootq + 1)b(2 less than or equal to b less than or equal to rootq - 1) or k = (q - 1)\rootqb + rootq + 1 and d = (rootq +1)b(2 less than or equal to b less than or equal to rootq - 2) are constructed by using certain reducible plane curves.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
