Description

Book Synopsis
A large portion of the book can be used as a textbook for graduate and upper level undergraduate students in mathematics, communication engineering, computer science and other fields. The remaining part can be used as references for specialists. Explicit construction and computation of finite fields are emphasized. In particular, the construction of irreducible polynomials and normal basis of finite field is included. A detailed treatment of optimal normal basis and Galoi's rings is included. It is the first time that the galois rings are in book form.

Table of Contents
Sets and Integers; Groups; Fields and Rings; Polynomials; Residue Class Rings; Structure of Finite Fields; Further Properties of Finite Fields; Bases; Factoring Polynomials over Finite Fields; Irreducible Polynomials over Finite Fields; Quadratic Forms over Finite Fields; More Group Theory and Ring Theory; Hensel's Lemma and Hensel Lift; Galois Rings.

Finite Fields And Galois Rings

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    A Hardback by Zhe-xian Wan

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      Publisher: World Scientific Publishing Co Pte Ltd
      Publication Date: Publication Date: 14/09/2011
      ISBN13: 9789814366342, 978-9814366342
      ISBN10: 981436634X

      Description

      Book Synopsis
      A large portion of the book can be used as a textbook for graduate and upper level undergraduate students in mathematics, communication engineering, computer science and other fields. The remaining part can be used as references for specialists. Explicit construction and computation of finite fields are emphasized. In particular, the construction of irreducible polynomials and normal basis of finite field is included. A detailed treatment of optimal normal basis and Galoi's rings is included. It is the first time that the galois rings are in book form.

      Table of Contents
      Sets and Integers; Groups; Fields and Rings; Polynomials; Residue Class Rings; Structure of Finite Fields; Further Properties of Finite Fields; Bases; Factoring Polynomials over Finite Fields; Irreducible Polynomials over Finite Fields; Quadratic Forms over Finite Fields; More Group Theory and Ring Theory; Hensel's Lemma and Hensel Lift; Galois Rings.

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