New geometrical spectra of linear codes with applications to performance analysis

@article{Ma2013NewGS,
title={New geometrical spectra of linear codes with applications to performance analysis},
author={X. Ma and Jia Liu and Qiutao Zhuang and B. Bai},
journal={2013 IEEE Information Theory Workshop (ITW)},
year={2013},
pages={1-5}
}

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.