  In this paper, new enumerating functions for linear codes are defined,
including the triangle enumerating function and the tetrahedron enumerating
function, both of which can be computed using a trellis-based algorithm over
polynomial rings. The computational complexity is dominated by the complexity
of the trellis. In addition, we show that these new enumerating functions can
be used to improve existing performance bounds on the maximum likelihood
decoding.
