Let r > 0 be an integer, let Fq be a finite field of q elements, and let A be a nonempty proper subset of Fq. Moreover, let M be a random m× n rank-r matrix over Fq taken with uniform distribution. We prove, in a precise sense, that, as m, n → +∞ and r, q, A are fixed, the number of entries of M that belong to A approaches a normal distribution
On the distribution of the entries of a fixed-rank random matrix over a finite field / Sanna, Carlo. - In: FINITE FIELDS AND THEIR APPLICATIONS. - ISSN 1071-5797. - 93:(2024), pp. 1-15. [10.1016/j.ffa.2023.102333]
On the distribution of the entries of a fixed-rank random matrix over a finite field
Carlo Sanna
2024
Abstract
Let r > 0 be an integer, let Fq be a finite field of q elements, and let A be a nonempty proper subset of Fq. Moreover, let M be a random m× n rank-r matrix over Fq taken with uniform distribution. We prove, in a precise sense, that, as m, n → +∞ and r, q, A are fixed, the number of entries of M that belong to A approaches a normal distributionFile in questo prodotto:
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