编码与曲线朱迪·L.沃克书籍 pdf下载

●IAS/Park City Mathematics Institute
Preface
Chapter1.Introduction to Coding Theory
§1.1.Overview
§1.2.Cyclic Codes
Chapter2.Boundson Codes
§2.1.Bounds
§2.2.Asymptotic Bounds
Chapter3.Algebraic Curves
§3.1.Algebraically Closed Fields
§3.2.Curves and the Projective Plane
Chapter4.Nonsingularity and the Genus
§4.1.Nonsingularity
§4.2.Genus
Chapter5.Points, Functions, and Divisors on Curves
Chapter6.Algebraic Geometry Codes
Chapter7.Good Codes from Algebraic Geometry
Appendix A.Abstract Algebra Review
§A.1.Groups
§A.2.Rings, Fields, Ideals, and Factor Rings
§A.3.Vector Spaces
§A.4.Homomorphisms and Isomorphisms
Appendix B.Finite Fields
§B.1.Background and Terminology
§B.2.Classification of Finite Fields
§B.3.Optional Exercises
Appendix 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
Bibliography