Coding theory: Tutorial & survey

Annual Symposium on Foundations of Computer Science - Proceedings

Volumn , Issue , 2001, Pages 36-53

  Sudan, M ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SCIENCE; DECODING; ERROR CORRECTION;

ERROR-CORRECTING CODES;

ENCODING (SYMBOLS);

EID: 0035162928     PISSN: 02725428     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/sfcs.2001.959879     Document Type: Conference Paper

References (101)

1. Reconstructing algebraic functions from mixed data
2. The hardness of approximating problems defined by linear constraints
3. Improved low-degree testing and its applications
4. A hensel lifting to replace factorization in list decoding of algebraic-geometric and reed-solomon codes
5. Linear-time decodable, capacity achieving binary codes with exponentially falling error probability
6. New upper bounds for error correcting codes
7. Hiding instances in multioracle queries
8. Factoring polynomials over large finite fields
9. Bounded distance +1 soft-decision Reed-Solomon decoding
10. On the inherent intractability of certain coding problems (Corresp.)
11. Finding smooth integers in short intervals using CRT decoding
12. On a class of error correcting binary group codes
13. An algebraic approach to the association schemes of coding theory
14. Approximating-CVP to within almost-polynomial factors is NP-hard
15. The parametrized complexity of some fundamental problems in coding theory
16. Two algorithms for the decoding of linear codes
17. Hardness of approximating the minimum distance of a linear code
18. On the hardness of computing the permanent of random matrices
19. Computing roots of polynomials over function fields of curves
20. A tower of artin-schreier extensions of function fields attaining the drinfeld-vlǎdut bound
21. Self-testing/correcting for polynomials and for approximate functions
22. Highly resilient correctors for multivariate polynomials
23. A comparison of signalling alphabets
24. Notes on digital coding
25. A hard-core predicate for all one-way functions
26. Chinese remaindering with errors
27. Codes on algebraic curves
28. m symbols
29. Factorization of polynomials over a finite field and the solution of systems of algebraic equations
30. Expander-based constructions of efficiently decodable codes
31. Improved decoding of Reed-Solomon and algebraic-geometric codes
32. List decoding algorithms for certain concatenated codes
33. Soft-decision decoding of Chinese Remainder codes
34. Error Detecting and Error Correcting Codes
35. Alternant codes
36. Codes correcteurs d'erreurs
37. A new upper bound for error-correcting codes
38. A class of constructive asymptotically good algebraic codes
39. Polynomial-time reductions from multivariate to bi- and univariate integral polynomial factorization
40. Modular curves and codes with a polynomial construction
41. A unified description of an error locating procedure for linear codes
42. Algebraic soft-decision decoding of Reed-Solomon codes
43. Factoring multivariate polynomials over finite fields
44. Nonexistence theorems for perfect error-correcting codes
45. Analysis of low density codes and improved designs using irregular graphs
46. Practical loss-resilient codes
47. A theorem on the distribution of weights in a systematic code
48. On a class of arithmetic codes and a decoding algorithm
49. Shift-register synthesis and BCH decoding
50. On the second step in the Guruswami-Sudan list decoding algorithm for agcodes
51. New upper bounds on the rate of a code via the Delsarte-Macwilliams inequalities
52. Application of Boolean algebra to switching circuit design and to error detection
53. Decoding Hermitian codes with Sudan's algorithm
54. A displacement structure approach to efficient list decoding of algebraic geometric codes
55. Encoding and error-correction procedures for Bose-Chaudhuri codes
56. Binary codes with specified minimum distance
57. A class of multiple-error-correcting codes and the decoding scheme
58. Polynomial codes over certain finite fields
59. The capacity of low-density parity-check codes under message-passing decoding
60. Design of capacity-approaching irregular low-density parity-check codes
61. Efficient decoding of Reed-Solomon codes beyond half the minimum distance
62. A mathematical theory of communication
63. Lower bounds to error probability for coding on discrete memoryless channels
64. List decoding of algebraic-geometric codes
65. Decoding Reed-Solomon codes beyond (d - 1)/2 and zeros of multivariate polynomials
66. Expander codes
67. A class of binary signalling alphabets
68. Linear-time encodable and decodable error-correcting codes
69. Decoding of Reed-Solomon codes beyond the error-correction bound
70. Decoding of Reed-Solomon codes beyond the error-correction diameter
71. Pseudorandom generators without the XOR lemma
72. A recursive approach to low complexity, codes
73. Extractor Codes
74. On the nonexistence of perfect codes over finite fields
75. Modular curves, Shimura curves, and codes better than the Varshamov-Gilbert bound
76. Algorithmic complexity in coding theory and the minimum distance problem
77. Estimate of the number of signals in error correcting codes
78. List Decoding
79. Efficient list decoding of algebraic geometric codes beyond the error correction bound