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

New Geometrical Spectra of Linear Codes with Applications to Performance Analysis