  The pairing symmetry is one of the major issues in the study of iron-based
superconductors. We adopt a minimal two-band tight-binding model with various
channels of pairing interaction, and derive a set of two-band Bogoliubov-de
Gennes (BdG) equations. The BdG equations are implemented in real space and
then solved self-consistently via exact diagonalization. In the uniform case,
we find that the $d_{x^2-y^2}$-wave pairing state is most favorable for a
nearest-neighbor pairing interaction while the $s_{x^2y^2}$-wave pairing state
is most favorable for a next-nearest-neighbor pairing interaction. The is
consistent with that reported by Seo {\em et al.} [Phys. Rev. Lett. {\bf 101},
206404 (2008)]. We then proceed to study the local electronic structure around
a magnetic vortex core for both $d_{x^2-y^2}$-wave and $s_{x^2y^2}$-wave
pairing symmetry in the mixed state. It is found from the local density of
states (LDOS) spectra and its spatial variation that the resonance core states
near the Fermi energy for the $d_{x^2-y^2}$-wave pairing symmetry are bound
while those for the $s_{x^2y^2}$-wave pairing symmetry can evolve from the
localized states into extended ones with varying electron filling factor.
Furthermore, by including an effective exchange interaction, the emergent
antiferromagnetic spin-density-wave (SDW) order can suppress the resonance core
states, which provides one possible avenue to understand the absence of
resonance peak as revealed by recent scanning tunneling microscopy experiment
(STM) by Yin {\em et al.} [Phys. Rev. Lett. {\bf 102}, 097002 (2009)].
