Topics in Galois Fields
Publication year: 2020
ISBN: 978-3-030-60806-4
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Provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures. It also covers important advanced topics which are not yet found in textbooks: the primitive normal basis theorem, the existence of primitive elements in affine hyperplanes, and the Niederreiter method for factoring polynomials over finite fields. We give streamlined and/or clearer proofs for many fundamental results and treat some classical material in an innovative manner. In particular, we emphasize the interplay between arithmetical and structural results, and we introduce Berlekamp algebras in a novel way which provides a deeper understanding of Berlekamp's celebrated factorization algorithm.
Subject: Mathematics and Statistics, Field Theory and Polynomials, Number Theory, Combinatorics, Mathematics of Computing, Algebraic extension, Bases and generators, Galois fields, Mathematics of computation, Polynomials, Finite fields, Algebra, Discrete mathematics, Computational algebra
