  A study of 4$\alpha$ linear-chain structure in high-lying collective
excitation states of $^{16}$O with a covariant density functional theory is
presented. The low-spin states are obtained by configuration mixing of
particle-number and angular-momentum projected quadrupole deformed mean-field
states with generator coordinate method. The high-spin states are determined by
cranking calculations. These two calculations are based on the same energy
density functional PC-PK1. We have found a rotational band at low-spin with the
dominated intrinsic configuration considered to be the one that 4$\alpha$
clusters stay along a common axis. The strongly deformed rod shape also appears
in the high-spin region with the angular momentum $13-18\hbar$; however whether
the state is pure $4\alpha$ linear chain or not is less obvious than that in
the low-spin states.
