  Asymptotic concentration behaviors of linear combinations of weight
distributions on the random linear code ensemble are presented. Many important
properties of a binary linear code can be expressed as the form of a linear
combination of weight distributions such as number of codewords, undetected
error probability and upper bound on the maximum likelihood error probability.
The key in this analysis is the covariance formula of weight distributions of
the random linear code ensemble, which reveals the second-order statistics of a
linear function of the weight distributions. Based on the covariance formula,
several expressions of the asymptotic concentration rate, which indicate the
speed of convergence to the average, are derived.
