Distribution of matrices in a finite field
نویسندگان
چکیده
منابع مشابه
Stochastic Matrices in a Finite Field
Abstract: In this project we will explore the properties of stochastic matrices in both the real and the finite fields. We first explore what properties 2 2 stochastic matrices in the real field have and then exam if they hold in the finite fields. We will prove how, given the conditions of a finite field, properties hold or fail to hold. We will extend our scope to 3 3 stochastic matrices ...
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Shift registers/Primitive polynomials find applications in various branches of Mathematics, Coding Theory and Cryptography. Matrix analogues of primitive polynomials do exist. In this paper, an algorithmic approach to generating all such matrices over GF(2) has been presented. A technique for counting all such n× n matrices over GF(2) is also presented. The technique may be easily extended to o...
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Given a finite field F and a positive integer n, we give a procedure to count the n×n matrices with entries in F with all eigenvalues in the field. We give an exact value for any field for values of n up to 4, and prove that for fixed n, as the size of the field increases, the proportion of matrices with all eigenvalues in the field approaches 1/n!. As a corollary, we show that for large fields...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1956
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1956.6.225