A First Course in Coding TheoryAlgebraic coding theory is a new and rapidly developing subject, popular for its many practical applications and for its fascinatingly rich mathematical structure. This book provides an elementary yet rigorous introduction to the theory of error-correcting codes. Based on courses given by the author over several years to advanced undergraduates and first-year graduated students, this guide includes a large number of exercises, all with solutions, making the book highly suitable for individual study. |
Contents
Codes and Latin squares | 113 |
A doubleerror correcting decimal code and | 125 |
Cyclic codes | 141 |
Weight enumerators | 165 |
The main linear coding theory problem | 175 |
MDS codes | 191 |
Concluding remarks related topics and further | 201 |
Solutions to exercises | 211 |
| 243 | |
| 249 | |
Common terms and phrases
a₁ algorithm B₄(n BCH codes binary code binary Golay code binary Hamming code binary linear code binary symmetric channel C₁ Chapter code of Example code of length codeword coding theory columns of H construct Corollary coset leaders cyclic code d)-code decoding defined denote digits encoded equations equivalent Exercise finite field g₁(x given gives Golay code Hamming code Hamming code Ham Hence irreducible polynomials k]-code Latin squares Lemma linear code linearly independent MacWilliams and Sloane matrix H max3 MDS codes minimum distance modulo MOLS of order non-zero elements optimal order q orthogonal pair of MOLS parameters parity-check matrix perfect codes prime number prime power problem proof of Theorem q-ary received vector Remark repetition code rows of G scalar multiple Show single error sphere-packing bound standard array standard form subspace symbols syndrome ternary Theorem 8.4 values Wc(z weight enumerator x₁ zero