Error-correcting codes and finite fields
Choice Reviews Online · 1993
Introduction Block codes, weight, and distance Linear codes Error processing for linear codes Hamming codes Appendix: Linear algebra Introduction and an example Euclid's algorithm Invertible and irreducible elements The construction of finite fields The structure of finite fields Roots of polynomials Primitive elements Appendix: Polynomials over a field BCH-codes as subcodes of Hamming codes BCH codes as polynomial codes Decoding BCH codes (1) the fundamental equation Decoding BCH codes: (2) an error processing algorithm Reed-Solomon codes and burst error correction Bounds on codes Classical Goppa codes Classical Goppa codes: error processing Introduction to algebraic curves Functions on algebraic curves A survey of the theory of algebraic curves Geometric Goppa codes An error processor for geometric Goppa codes.