The list decoding error probability of linear codes over the erasure channel

In this paper, we study the list decoding error probability of a linear code over the erasure channel. The notion of L-incorrigible sets of a linear code is introduced to characterize its performance under list decoding. The L-incorrigible set distribution of a linear code can also be used to completely determine its decoding error probability under maximum likelihood decoding over the erasure channel. Furthermore, we show that the L-incorrigible set distribution of a linear code can be determined by its support weight distribution. Finally, the error exponent of the unsuccessful decoding probability under optimal decoding for the ensemble of all [n, nR] linear codes is determined.