Introduction to Coding TheorySpringer Science & Business Media, 6.12.2012 - 186 sivua The first edition of this book was conceived in 1981 as an alternative to outdated, oversized, or overly specialized textbooks in this area of discrete mathematics-a field that is still growing in importance as the need for mathematicians and computer scientists in industry continues to grow. The body of the book consists of two parts: a rigorous, mathematically oriented first course in coding theory followed by introductions to special topics. The second edition has been largely expanded and revised. The main editions in the second edition are: (1) a long section on the binary Golay code; (2) a section on Kerdock codes; (3) a treatment of the Van Lint-Wilson bound for the minimum distance of cyclic codes; (4) a section on binary cyclic codes of even length; (5) an introduction to algebraic geometry codes. Eindhoven J. H. VAN LINT November 1991 Preface to the First Edition Coding theory is still a young subject. One can safely say that it was born in 1948. It is not surprising that it has not yet become a fixed topic in the curriculum of most universities. On the other hand, it is obvious that discrete mathematics is rapidly growing in importance. The growing need for mathe maticians and computer scientists in industry will lead to an increase in courses offered in the area of discrete mathematics. One of the most suitable and fascinating is, indeed, coding theory. |
Sisältö
1 | |
CHAPTER | 4 |
CHAPTER 2 | 17 |
CHAPTER 3 | 31 |
CHAPTER 8 | 58 |
CHAPTER 6 | 75 |
8 | 93 |
Goppa Codes | 118 |
CHAPTER 10 | 133 |
14 | 140 |
Hints and Solutions to Problems | 155 |
429 | 160 |
174 | |
www | 175 |
179 | |
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a₁ AG(m algebraic automorphism b₁ BCH bound BCH code binary code binary cyclic code block codes C₁ C₂ called Chapter CNAF code of length code over F codeword coding theory coefficients columns consider construction convolutional codes corresponding cosets cyclic code decoding define Definition denote designed distance dimension elements of F encoded equation example F₂ following theorem function g₁(x Gilbert bound Golay code Goppa codes Hamming code Hence idempotent integer irreducible polynomials Krawtchouk Lemma Let q linear code linear combination matrix H minimal polynomial minimum distance multiplication N₁ nonzero nth root obtained parity check matrix perfect code permutation Plotkin bound polynomial g(x polynomial of degree positions primitive element primitive nth root QR code reader representation resp root of unity rows of G Section sequence Show ternary uniformly packed codes weight enumerator words of weight yields zeros