編碼與曲線（影印版）

IAS/Park City Mathematics Institute
Preface
Chapter 1．Introduction to Coding Theory
1．1．Overview
1．2．Cyclic Codes
Chapter 2．Bounds on Codes
2．1．Bounds
2．2．Asymptotic Bounds
Chapter 3．Algebraic Curves
3．1．Algebraically Closed Fields
3．2．Curves and the Projective Plane
Chapter 4．Nonsingularity and the Genus
4．1．Nonsingularity
4．2．Genus
Chapter 5．Points， Functions， and Divisors on Curves
Chapter 6．Algebraic Geometry Codes
Chapter 7．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．OptionalExercises
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