  The complexity of software implementations of MDS erasure codes mainly
depends on the efficiency of the finite field operations implementation. In
this paper, we propose a method to reduce the complexity of the finite field
multiplication by using fast transforms between a field and a ring to perform
the multiplication in a ring. We show that moving to a ring reduces the
complexity of the operations. Then, we show that this construction allows the
use of simple scheduling to reduce the number of operations.
