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Topics in Galois Fields (Hardcover, 1st ed. 2020)
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Topics in Galois Fields (Hardcover, 1st ed. 2020)
Series: Algorithms and Computation in Mathematics, 29
Expected to ship within 12 - 19 working days
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This monograph 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.
The book provides a thorough grounding in finite field theory for
graduate students and researchers in mathematics. In view of its
emphasis on applicable and computational aspects, it is also useful
for readers working in information and communication engineering,
for instance, in signal processing, coding theory, cryptography or
computer science.
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