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＜電子ブック＞
Algebraic Function Fields and Codes / by Henning Stichtenoth
(Graduate Texts in Mathematics. ISSN:21975612 ; 254)

版	2nd ed. 2009.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2009
本文言語	英語
大きさ	XIV, 360 p : online resource
著者標目	*Stichtenoth, Henning author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Algebraic geometry LCSH:Data structures (Computer science) LCSH:Information theory LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Engineering mathematics LCSH:Engineering -- Data processing  全ての件名で検索 FREE:Algebra FREE:Algebraic Geometry FREE:Data Structures and Information Theory FREE:Mathematical Applications in Computer Science FREE:Mathematical and Computational Engineering Applications
一般注記	Foundations of the Theory of Algebraic Function Fields -- Algebraic Geometry Codes -- Extensions of Algebraic Function Fields -- Differentials of Algebraic Function Fields -- Algebraic Function Fields over Finite Constant Fields -- Examples of Algebraic Function Fields -- Asymptotic Bounds for the Number of Rational Places -- More about Algebraic Geometry Codes -- Subfield Subcodes and Trace Codes The theory of algebraic function fields has its origins in number theory, complex analysis (compact Riemann surfaces), and algebraic geometry. Since about 1980, function fields have found surprising applications in other branches of mathematics such as coding theory, cryptography, sphere packings and others. The main objective of this book is to provide a purely algebraic, self-contained and in-depth exposition of the theory of function fields. This new edition, published in the series Graduate Texts in Mathematics, has been considerably expanded. Moreover, the present edition contains numerous exercises. Some of them are fairly easy and help the reader to understand the basic material. Other exercises are more advanced and cover additional material which could not be included in the text. This volume is mainly addressed to graduate students in mathematics and theoretical computer science, cryptography, coding theory and electrical engineering HTTP:URL=https://doi.org/10.1007/978-3-540-76878-4

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