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- catalog abstract ""This monograph is based on a series of lectures the author gave as part of the IAS/PCMI program on arithmetic algebraic geometry. Here, the reader is introduced to the exciting field of algebraic geometric coding theory. Presenting the material in the same conversational tone of the lectures, the author covers linear codes, including cyclic codes, and both bounds and asymptotic bounds on the parameters of codes. Algebraic geometry is introduced, with particular attention given to projective curves, rational functions and divisors. The construction of algebraic geometric codes is given, and the Tsfasman-Vladut-Zink result mentioned above it discussed."--Jacket.".
- catalog contributor b12084405.
- catalog created "c2000.".
- catalog date "2000".
- catalog date "c2000.".
- catalog dateCopyrighted "c2000.".
- catalog description ""This monograph is based on a series of lectures the author gave as part of the IAS/PCMI program on arithmetic algebraic geometry. Here, the reader is introduced to the exciting field of algebraic geometric coding theory. Presenting the material in the same conversational tone of the lectures, the author covers linear codes, including cyclic codes, and both bounds and asymptotic bounds on the parameters of codes. Algebraic geometry is introduced, with particular attention given to projective curves, rational functions and divisors. The construction of algebraic geometric codes is given, and the Tsfasman-Vladut-Zink result mentioned above it discussed."--Jacket.".
- catalog description "IAS/Park City Mathematics Institute -- Ch. 1. Introduction to Coding Theory -- 1.1. Overview -- 1.2. Cyclic Codes -- Ch. 2. Bounds on Codes -- 2.1. Bounds -- 2.2. Asymptotic Bounds -- Ch. 3. Algebraic Curves -- 3.1. Algebraically Closed Fields -- 3.2. Curves and the Projective Plane -- Ch. 4. Nonsingularity and the Genus -- 4.1. Nonsingularity -- 4.2. Genus -- Ch. 5. Points, Functions, and Divisors on Curves -- Ch. 6. Algebraic Geometry Codes -- Ch. 7. Good Codes from Algebraic Geometry -- App. A. Abstract Algebra Review -- A.1. Groups -- A.2. Rings, Fields, Ideals, and Factor Rings -- A.3. Vector Spaces -- A.4. Homomorphisms and Isomorphisms. App. B. Finite Fields -- B.1. Background and Terminology -- B.2. Classification of Finite Fields -- B.3. Optional Exercises. App. C. Projects -- C.1. Dual Codes and Parity Check Matrices -- C.2. BCH Codes -- C.3. Hamming Codes -- C.4. Golay Codes -- C.5. MDS Codes -- C.6. Nonlinear Codes.".
- catalog description "Includes bibliographical references (p. 65-66).".
- catalog extent "xii, 66 p. :".
- catalog identifier "082182628X (softcover : alk. paper)".
- catalog isPartOf "Student mathematical library ; v. 7.".
- catalog isPartOf "Student mathematical library, 1520-9121 ; v. 7. IAS/Park City mathematical subseries".
- catalog isPartOf "Student mathematical library. IAS/Park City mathematical subseries.".
- catalog issued "2000".
- catalog issued "c2000.".
- catalog language "eng".
- catalog publisher "Providence, R.I. : American Mathematical Society,".
- catalog subject "003/.54 21".
- catalog subject "Coding theory.".
- catalog subject "Curves, Algebraic.".
- catalog subject "QA268 .W345 2000".
- catalog tableOfContents "IAS/Park City Mathematics Institute -- Ch. 1. Introduction to Coding Theory -- 1.1. Overview -- 1.2. Cyclic Codes -- Ch. 2. Bounds on Codes -- 2.1. Bounds -- 2.2. Asymptotic Bounds -- Ch. 3. Algebraic Curves -- 3.1. Algebraically Closed Fields -- 3.2. Curves and the Projective Plane -- Ch. 4. Nonsingularity and the Genus -- 4.1. Nonsingularity -- 4.2. Genus -- Ch. 5. Points, Functions, and Divisors on Curves -- Ch. 6. Algebraic Geometry Codes -- Ch. 7. Good Codes from Algebraic Geometry -- App. A. Abstract Algebra Review -- A.1. Groups -- A.2. Rings, Fields, Ideals, and Factor Rings -- A.3. Vector Spaces -- A.4. Homomorphisms and Isomorphisms. App. B. Finite Fields -- B.1. Background and Terminology -- B.2. Classification of Finite Fields -- B.3. Optional Exercises. App. C. Projects -- C.1. Dual Codes and Parity Check Matrices -- C.2. BCH Codes -- C.3. Hamming Codes -- C.4. Golay Codes -- C.5. MDS Codes -- C.6. Nonlinear Codes.".
- catalog title "Codes and curves / Judy L. Walker.".
- catalog type "text".