The theory of error correcting codes / F.J. MacWilliams, N.J.A. Sloane.
Spremljeno u:
Glavni autori: | , |
---|---|
Format: | e-knjiga |
Jezik: | English |
Izdano: |
Amsterdam ; New York : New York :
North-Holland Pub. Co. ; Sole distributors for the U.S.A. and Canada, Elsevier/North-Holland,
1977.
|
Serija: | North-Holland mathematical library ;
v. 16. |
Teme: | |
Online pristup: | Click for online access |
Sadržaj:
- Front Cover; The Theory of Error-Correcting Codes; Copyright Page; Preface; Preface to the third printing; Contents; Chapter 1. Linear codes; 1. Linear codes; 2. Properties of a linear code; 3. At the receiving end; 4. More about decoding a linear code; 5. Error probability; 6. Shannon's theorem on the existence of good codes; 7. Hamming codes; 8. The dual code; 9. Construction of new codes from old (II); 10. Some general properties of a linear code; 11. Summary of Chapter 1; Notes on Chapter 1; Chapter 2. Nonlinear codes, Hadamard matrices, designs and the Golay code; 1. Nonlinear codes
- 2. The Plotkin bound3. Hadamard matrices and Hadamard codes; 4. Conferences matrices; 5. t-designs; 6. An introduction to the binary Golay code; 7. The Steiner system S(5, 6, 12), and nonlinear single-error correcting codes; 8. An introduction to the Nordstrom-Robinson code; 9. Construction of new codes from old (III); Notes on Chapter 2; Chapter 3. An introduction to BCH codes and finite fields; 1. Double-error-correcting BCH codes (I); 2. Construction of the field GF(16); 3. Double-error-correcting BCH codes (II); 4. Computing in a finite field; Notes on Chapter 3; Chapter 4. Finite fields
- 1. Introduction2. Finite fields: the basic theory; 3. Minimal polynomials; 4. How to find irreducible polynomials; 5. Tables of small fields; 6. The automorphism group of GF(pm); 7. The number of irreducible polynomials; 8. Bases of GF(pm) over GF(p); 9. Linearized polynomials and normal bases; Notes on Chapter 4; Chapter 5. Dual codes and their weight distribution; 1. Introduction; 2. Weight distribution of the dual of a binary linear code; 3. The group algebra; 4. Characters; 5. MacWilliams theorem for nonlinear codes; 6. Generalized MacWilliams theorems for linear codes
- 7. Properties of Krawtchouk polynomialsNotes on Chapter 5; Chapter 6. Codes. designs and perfect codes; 1. Introduction; 2. Four fundamental parameters of a code; 3. An explicit formula for the weight and distance distribution; 4. Designs from codes when s = d'; 5. The dual code also gives designs; 6. Weight distribution of translates of a code; 7. Designs from nonlinear codes when s' = d; 8. Perfect codes; 9. Codes over GF(q); 10. There are no more perfect codes; Notes on Chapter 6; Chapter 7. Cyclic codes; 1. Introduction; 2. Definition of a cyclic code; 3. Generator polynomial
- 4. The check polynomial5. Factors of Xn
- 1; 6. t-error-correcting BCH codes; 7. Using a matrix over GF(qn) to define a code over GF(q); 8. Encoding cyclic codes; Notes on Chapter 7; Chapter 8. Cyclic codes (contd.): Idempotents and Mattson-Solomon polynomials; 1. Introduction; 2. Idempotents; 3. Minimal ideals. irreducible codes. and primitive idempotents; 4. Weight distribution of minimal codes; 5. The automorphism group of a code; 6. The Mattson-Solomon polynomial; 7. Some weight distributions; Notes on Chapter 8; Chapter 9. BCH codes; 1. Introduction