Ebook: Foundations of Coding Theory
- Tags: Data Structures Cryptology and Information Theory, Philosophy of Education, Theory of Computation
- Series: Episteme 1
- Year: 1974
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
During the sixteenth century, Cardano wrote a fascinating work called The Book on Games of Chance. In it he gives an extremely candid recount ing and personal appraisal of some aspects of his most remarkable life. * One feature of the book is striking for the modern scientist or mathemati cian accustomed to current publishing practices. It is brought out during Cardano's discussion of his investigations of certain special questions of applied probability, namely, the question of how to win at gambling. His technique is simplicity itself: in fine reportorial style he reveals his proposed strategy for a particular gambling game, giving marvelous motivating arguments which induce the reader to feel warm, heartfelt support for the projected strategy. Then with all the drama that only a ringside seat observation can bring, Cardano announces that he tried the strategy at the casino and ended up borrowing his taxi fare. Undaunted by failure, he analyzes his now fire-tested strategy in detail, mounts new and per suasive arguments, and, ablaze with fresh optimism and replenished resources, charges off to the fray determined to now succeed where he had so often failed before. Along the way, Cardano developed a number of valuable insights about games of chance and produced useful research results which presumably would be of interest in our present-day society. However, he could never publish the results today in journals with all the flair, the mistakes, the failures and minor successes which he exhibits in his book.
Content:
Front Matter....Pages I-XIII
Front Matter....Pages 1-1
Basic Problems of Abstract Coding Theory....Pages 3-15
Basic Properties of Error-Correcting Codes....Pages 17-36
Front Matter....Pages 37-37
Overview....Pages 39-40
A Study of Error-Correcting Codes, I....Pages 41-59
A Study of Error-Correcting Codes, II: Decodability Properties....Pages 61-82
A Study of Error-Correcting Codes, III: Synchronizability and Comma-Freedom....Pages 83-96
A Study of Error-Correcting Codes, IV: Code Properties and Unambiguous Sets....Pages 97-105
Some General Results of Abstract Coding Theory with Applications to the Study of Codes for the Correction of Synchronization Errors....Pages 107-121
Front Matter....Pages 123-123
Overview....Pages 125-127
The Sardinas/Patterson and Levenshtein Theorems....Pages 129-145
Generalization of Tests for Certain Properties of Variable-Length Codes....Pages 147-172
On a Family of Error Correcting and Synchronizable Codes....Pages 173-192
A Family of Codes for the Correction of Substitution and Synchronization Errors....Pages 193-204
Epilogue....Pages 205-206
Back Matter....Pages 207-216
Content:
Front Matter....Pages I-XIII
Front Matter....Pages 1-1
Basic Problems of Abstract Coding Theory....Pages 3-15
Basic Properties of Error-Correcting Codes....Pages 17-36
Front Matter....Pages 37-37
Overview....Pages 39-40
A Study of Error-Correcting Codes, I....Pages 41-59
A Study of Error-Correcting Codes, II: Decodability Properties....Pages 61-82
A Study of Error-Correcting Codes, III: Synchronizability and Comma-Freedom....Pages 83-96
A Study of Error-Correcting Codes, IV: Code Properties and Unambiguous Sets....Pages 97-105
Some General Results of Abstract Coding Theory with Applications to the Study of Codes for the Correction of Synchronization Errors....Pages 107-121
Front Matter....Pages 123-123
Overview....Pages 125-127
The Sardinas/Patterson and Levenshtein Theorems....Pages 129-145
Generalization of Tests for Certain Properties of Variable-Length Codes....Pages 147-172
On a Family of Error Correcting and Synchronizable Codes....Pages 173-192
A Family of Codes for the Correction of Substitution and Synchronization Errors....Pages 193-204
Epilogue....Pages 205-206
Back Matter....Pages 207-216
....