Tail-biting-trellis representations of codes allow for iterative decoding algorithms, which are limited in effectiveness by the presence of pseudocodewords. We introduce a multivariate weight enumerator that keeps track of these pseudocodewords. This enumerator is invariant under many linear transformations, often enabling us to compute it exactly. The extended binary Golay code has a particularly nice tail-biting-trellis and a famous unsolved question is to determine its minimal AWGN pseudodistance. The new enumerator provides an inroad to this problem.
Nigel Boston. "A Multivariate Weight Enumerator for Tail-biting Trellis Pseudocodewords." J. Gen. Lie Theory Appl. 9 (S1) 1 - 4, 2015. https://doi.org/10.4172/1736-4337.S1-004