For and pick uniformly at random vectors in and let be the orthogonal complement of their span. Given with , let be the random variable that counts the number of words in of Hamming weight (where is assumed to be an even integer). Linial and Mosheiff [Random Struct. Algorithms. 62 (2023), 68Ű-130] determined the asymptotics of the moments of of all orders . In this paper we extend their estimates up to moments of linear order. Our key observation is that the behavior of the suitably normalized moment of is essentially determined by the norm of the Krawtchouk polynomial .

中文翻译：

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随机线性码和 Krawtchouk 多项式的权重分布

为了和随机均匀挑选向量在然后让是它们跨度的正交补集。给定和， 让是计算单词数量的随机变量汉明重量（在哪里假设为偶数）。 Linial 和 Mosheiff [随机结构。算法。 62 (2023), 68Ű-130] 确定了矩的渐近所有订单中。在本文中，我们将他们的估计扩展到线性阶矩。我们的主要观察是，适当标准化的行为的时刻本质上是由Krawtchouk 多项式的范数。