随机线性编码序列上权分布线性组合的渐近集中行为
Asymptotic Concentration Behaviors of Linear Combinations of Weight Distributions on Random Linear Code Ensemble
摘要：
研究了随机线性码集合上权分布线性组合的渐近集中行为。二进制线性码的许多重要性质可以表示为权重分布的线性组合的形式，例如码字的数量、未检测到的错误概率和最大似然错误概率的上界。该分析的关键是随机线性码集合的权重分布的协方差公式，该公式揭示了权重分布的线性函数的二阶统计量。基于协方差公式，导出了渐近集中率的几个表达式，它表示收敛到平均值的速度。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
