On bicovering arcs and small complete caps
(joint work with Massimo Giulietti)
Bicovering arcs in Galois ane planes of odd order are powerful tools for the construction of
complete caps in spaces of higher dimensions. In this work bicovering property of arcs contained
in elliptic cubic curves are investigated. As a result, bicovering k-arcs in AG(2; q) are obtained in
the case that q 1 has a prime divisor m with 7 < m < (1=8)q1=4. In some cases these arcs give
the smallest known complete caps of size kq(N2)=2 in AG(N; q) for N 0 (mod 4).