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Foundations of Coding Theory

  • Book
  • © 1974

Overview

Editors:
  1. William E. Hartnett

    1. Dept. of Mathematics, State University College, Plattsburgh, USA

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Part of the book series: Episteme (EPIS, volume 1)

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Table of contents (14 chapters)

  1. Front Matter

    Pages I-XIII
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  2. Introduction

    1. Front Matter

      Pages 1-1
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    2. Basic Problems of Abstract Coding Theory

      • W. E. Hartnett
      Pages 3-15

    3. Basic Properties of Error-Correcting Codes

      • L. Calabi, L. K. Arquette
      Pages 17-36

  3. Theoretical Studies

    1. Front Matter

      Pages 37-37
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    2. Overview

      • William E. Hartnett
      Pages 39-40

    3. A Study of Error-Correcting Codes, I

      • L. Calabi, L. K. Arquette
      Pages 41-59

    4. A Study of Error-Correcting Codes, II: Decodability Properties

      • L. K. Arquette, W. E. Hartnett
      Pages 61-82

    5. A Study of Error-Correcting Codes, III: Synchronizability and Comma-Freedom

      • L. Arquette, L. Calabi, W. E. Hartnett
      Pages 83-96

    6. A Study of Error-Correcting Codes, IV: Code Properties and Unambiguous Sets

      • L. Calabi, W. E. Hartnett
      Pages 97-105

    7. Some General Results of Abstract Coding Theory with Applications to the Study of Codes for the Correction of Synchronization Errors

      • L. Calabi, W. E. Hartnett
      Pages 107-121

  4. Tests and Constructions

    1. Front Matter

      Pages 123-123
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    2. Overview

      • William E. Hartnett
      Pages 125-127

    3. The Sardinas/Patterson and Levenshtein Theorems

      • J. A. Riley
      Pages 129-145

    4. Generalization of Tests for Certain Properties of Variable-Length Codes

      • W. E. Hartnett
      Pages 147-172

    5. On a Family of Error Correcting and Synchronizable Codes

      • T. Hatcher
      Pages 173-192

    6. A Family of Codes for the Correction of Substitution and Synchronization Errors

      • L. Calabi, W. E. Hartnett
      Pages 193-204

    7. Epilogue

      • William E. Hartnett
      Pages 205-206

  5. Back Matter

    Pages 207-216
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Keywords

About this book

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.

Editors and Affiliations

  • Dept. of Mathematics, State University College, Plattsburgh, USA

    William E. Hartnett

Bibliographic Information

  • Book Title: Foundations of Coding Theory

  • Editors: William E. Hartnett

  • Series Title: Episteme

  • DOI: https://doi.org/10.1007/978-94-010-2298-9

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: D. Reidel Publishing Company, Dordrecht, Holland 1974

  • Hardcover ISBN: 978-90-277-0536-5Due: 31 December 1974

  • Softcover ISBN: 978-94-010-2300-9Published: 12 October 2011

  • eBook ISBN: 978-94-010-2298-9Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: 236

  • Topics: Data Structures and Information Theory, Philosophy of Education, Theory of Computation

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