Galois groups of polynomials arising from circulant matrices
Galois_groups_of_polynomials_arising_from_circulant_matrices.pdf (152.6Kb)Date
2008Metadata
Show full item recordAbstract
Computing the Galois group of the splitting field of a given polynomial with integer coeffi-
cients is a classical problem in modern algebra. A theorem of Van der Waerden [Wae] asserts
that almost all (monic) polynomials in ℤ[x] have associated Galois group S(n), the symmetric
group on n letters. Thus, cases where the associated Galois group is different from S(n) are
rare. Nevertheless, examples of polynomials where the associated Galois group is not S(n) are
well-known.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.Collections
Related items
Showing items related by title, author, creator and subject.
-
A journey through Galois groups, irreducible polynomials and diophatine equations
(2017);Computing the Galois group of the splitting field of a given polynomial with integer coefficients over the rationals is a classical problem in modern algebra. A theorem of Van der Waerden [Wae] asserts that almost all ... -
Pascal polynomials over GF(2)
(Monterey, California. Naval Postgraduate School, 2008-06);The Discrete Logarithm Problem (DLP) is a fundamental cryptographic primitive. The DLP is defined for any cyclic group, specifically finite fields, whether the integers modulo a prime p or a polynomial field of characteristic ... -
Exploring fields with shift registers
(Monterey, California. Naval Postgraduate School, 2006-09);The S-Boxes used in the AES algorithm are generated by field extensions of the Galois field over two elements, called GF(2). Therefore, understanding the field extensions provides a method of analysis, potentially efficient ...
