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

被引：1
|
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.
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页数：7
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