A note on the distribution of weights of fixed-rank matrices over the binary field

被引：2

作者：

Sanna, Carlo ^{[1
]}

机构：

[1] Politecn Torino, Dept Math Sci, Corso Duca Abruzzi 24, I-10129 Turin, Italy

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2023年 / 87卷

关键词：

Binary matrix; Hamming weight; Normal distribution; Random matrix; Rank;

D O I：

10.1016/j.ffa.2022.102157

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let M be a random m x n rank -r matrix over the binary field F2, and let wt(M) be its Hamming weight, that is, the number of nonzero entries of M. We prove that, as m, n -> +infinity with r fixed and m/n tending to a constant, we have that wt(M) - 1-2-r 2 mn \/2-r(1-2-r) 4(m+n)mn converges in distribution to a standard normal random variable. (c) 2022 Elsevier Inc. All rights reserved.

引用

页数：7