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

Asymptotic Concentration Behaviors of Linear Combinations of Weight Distributions on Random Linear Code Ensemble