
The Geometry Of Curves Has Fascinated Mathematicians For 2500 Years, And The Theory Has Become Highly Abstract. Recently Links Have Been Made With The Subject Of Error Correction, Leading To The Creation Of Geometric Goppa Codes, A New And Important Area Of Coding Theory. This Book Is An Updated And Extended Version Of The Last Part Of The Successful Book Error-correcting Codes And Finite Fields. It Provides An Elementary Introduction To Goppa Codes, And Includes Many Examples, Calculations, And Applications. The Book Is In Two Parts With An Emphasis On Motivation, And Applications Of The Theory Take Precedence Over Proofs Of Theorems. The Formal Theory Is, However, Provided In The Second Part Of The Book, And Several Of The Concepts And Proofs Have Been Simplified Without Sacrificing Rigour.
This text investigates the intersection of algebraic geometry and coding theory, specifically focusing on the practical application of geometric Goppa codes. Oliver Pretzel, an experienced mathematician, utilizes his background in finite fields and error-correcting codes to bridge the gap between abstract geometric theory and real-world data transmission. The book argues that the complex geometry of curves can be made accessible for coding applications through a structured, two-part pedagogical approach that prioritizes motivation and utility over exhaustive formal proofs.
What You Will Find
Scope Limits
Experts and students frequently highlight this text as a highly accessible entry point into the specialized field of algebraic geometry in coding theory. Readers often note that the author's decision to prioritize motivation and examples makes the dense subject matter significantly more manageable for those without a pure mathematics background.
Page Count:
209
Publication Date:
1998-01-01
Publisher:
Clarendon Press
ISBN-10:
0191589047
ISBN-13:
9780191589041
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