Block Error-Correcting Codes: A Computational Primer (Universitext)

Error-correcting codes have been incorporated in numerous working communication and memory systems. This book covers the mathematical aspects of the theory of block error-correcting codes together, in mutual reinforcement, with computational discussions, implementations and examples of all relevant concepts, functions and algorithms. This combined approach facilitates the reading and understanding of the subject. The digital companion of the book is a non-printable .pdf document with hyperlinks. The examples included in the book can be run with just a mouse click and modified and saved by users for their own purpose. Preface......Page 3 Introduction......Page 7 Block Error-correcting Codes......Page 16 Basic concepts......Page 17 Linear codes......Page 35 Hadamard codes......Page 61 Parameter bounds......Page 71 Finite Fields......Page 90 Zn and Fp......Page 92 Construction of finite fields......Page 96 Structure of the multiplicative group of a finite field......Page 109 Minimum polynomial......Page 117 Cyclic Codes......Page 123 Generalities......Page 124 Effective factorization of Xn-1......Page 133 Roots of a cyclic code......Page 140 The Meggitt decoder......Page 149 Alternant Codes......Page 152 Definitions and examples......Page 154 Error location, error evaluation and the key equation......Page 164 The Berlekamp--Massey--Sugiyama algorithm......Page 172 The Peterson--Gorenstein--Zierler algorithm......Page 180 Appendix: The WIRIS/cc system......Page 185 Index of Symbols......Page 199 Alphabetic Index, Glossary and Notes......Page 202

error-correcting Codes Have Been Incorporated In Numerous Working Communication And Memory Systems. This Book Covers The Mathematical Aspects Of The Theory Of Block Error-correcting Codes Together, In Mutual Reinforcement, With Computational Discussions, Implementations And Examples Of All Relevant Concepts, Functions And Algorithms. This Combined Approach Facilitates The Reading And Understanding Of The Subject.

the Digital Companion Of The Book Is A Non-printable .pdf Document With Hyperlinks. The Examples Included In The Book Can Be Run With Just A Mouse Click And Modified And Saved By Users For Their Own Purpose.

Assume that you are asked to make sense of a 'sentence' like this: "Coding theary zs bodh wntelesting and challenning" (to take a simpler example than the Chinese saying in the quotation).