Complete arcs and complete caps from cubics with an isolated double point
Anbar, Nurdagul · Bartoli, Daniele · Giulietti, Massimo · Platoni, Irene
Original · EN
Small complete arcs and caps in Galois spaces over finite fields with characteristic greater than 3 are constructed from cubic curves with an isolated double point. For m a divisor of q+1, complete plane arcs of size approximately q/m are obtained, provided that (m,6)=1 and m<{14q¹/⁴. If in addition m=m₁m₂ with (m₁,m₂)=1, then complete caps of size approximately {m₁+m₂mqⁿ/² in affine spaces of dimension N≡ 0 4 are constructed.
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