  Degenerate quantum codes are codes that do not reveal the complete error
syndrome. Their ability to conceal the complete error syndrome makes them
powerful resources in certain quantum information processing tasks. In
particular, the most error-tolerant way to purify depolarized Bell states using
one-way communication known to date involves degenerate quantum codes. Here we
study three closely related purification schemes for depolarized GHZ states
shared among $m \geq 3$ players by means of degenerate quantum codes and
one-way classical communications. We find that our schemes tolerate more noise
than all other one-way schemes known to date, further demonstrating the
effectiveness of degenerate quantum codes in quantum information processing.
