The Distribution of the Rank of Random Matrices over a Finite Field
The Distribution of the Rank of Random Matrices over a Finite Field
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有限域上随机矩阵的秩分布
DOI：
10.1137/1113076
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发表时间：
1968
影响因子：
0.6
通讯作者：
G. V. Balakin
中科院分区：
文献类型：
--
作者：
G. V. Balakin
对于q 2，假设概率P（aj 1）满足不等式（log n）+/n<= P（aj 1）=< 1（log n）+/n，并且对于所有1，.，t，j 1，...，n中，矩阵A的最大秩概率的渐近性态在IN Kovalenko [1]和MV Kozlov [2]的文章中得到。则在更严格的条件下，δ =< P（aj 1）__<！6，6是一个固定的数字，IN Kovalenko 3]找到了矩阵A在域GF（2）上的秩的分布。本文考虑q，（log n+ x）/n的情况，其中x是一个固定数。
For q 2 under the assumption that the probabilities P (aj 1) satisfy the inequalities (log n)+/n<= P (aij 1)=< 1 (log n)+/n and are not necessarily identical for all 1,..., t, j 1,..., n, the asymp-totic behavior of the probability of maximal rank of thematrix A was found in the papers of IN Kovalenko [1] and MV Kozlov 2]. Then under the more stringent condition 6=< P (aj 1) __<!-6, 6 a fixed number, IN Kovalenko 3] found thedistribution of the rank of the matrix A over the field GF (2). In this note the case q,(log n+ x)/n is considered, where x is a fixed number.