Introduction to Coding Theory

An Elementary Introduction to Coding. The Concept of Coding. Binary Linear Codes. General Linear Codes. Reed-Solomon Codes. Recursive Construction I. Universal Hashing. Designs and the Binary Golay Code. Shannon Entropy. Asymptotic Results. 3-Dimensional Codes, Projective Planes. Summary and Outlook. The Theory of Codes and Their Applications. Subfield Codes and Trace Codes. Cyclic Codes. Recursive Constructions, Covering Radius. OA in Statistics and Computer Science. The Geometric Description of Codes. Additive Codes. Algebraic Curves. Introduction. Applications to Coding Theory.

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Cyclotomic Cosets;Reed Solomon Codes;linear;Linear Code;code;Hash Families;reed;Residue Class Field;solomon;BCH Code;cyclic;Extended Reed Solomon Codes;orthogonal;Ternary Golay Code;array;Cyclic Codes;minimum;Binary Linear Codes;distance;Orthogonal Arrays;generator;Reed Muller Codes;Juergen Bierbrauer;Irreducible Polynomial;coding theory;Binary Hamming Codes;algebraic curves;Minimal Polynomial;discrete mathematics;Hamming Code;Simplex Code;Rational Function Field;Galois Closure;Linearly Independent;Affine Equation;Fano Plane;Riemann Hurwitz Formula;Nonzero Codeword;Nordstrom Robinson Code