目次

Linear Codes. Nonlinear Codes, Hadamard Matrices, Designs and the GolayCode. An Introduction to BCH Codes and Finite Fields. Finite Fields. DualCodes and Their Weight Distribution. Codes, Designs and Perfect Codes. CyclicCodes. Cyclic Codes: Idempotents and Mattson-Solomon Polynomials. BCH Codes.Reed-Solomon and Justesen Codes. MDS Codes. Alternant, Goppa and OtherGeneralized BCH Codes. Reed-Muller Codes. First-Order Reed-Muller Codes.Second-Order Reed-Muller, Kerdock and Preparata Codes. Quadratic-ResidueCodes. Bounds on the Size of a Code. Methods for Combining Codes. Self-dualCodes and Invariant Theory. The Golay Codes. Association Schemes. Appendix A.Tables of the Best Codes Known. Appendix B. Finite Geometries. Bibliography.Index.