This text offers an introduction to error-correcting linear codes for researchers and graduate students in mathematics, computer science and engineering. The book differs from other standard texts in its emphasis on the classification of codes by means of isometry classes. The relevant algebraic are developed rigorously. Cyclic codes are discussed in great detail. In the last four chapters these isometry classes are enumerated, and representatives are constructed algorithmically.
Show that in a binary group block code either all the code words have even weight or half have even weight , half odd . ( Hint : Show that the code words of even ... Assume the matrix M given in the example of Section 3.6 . 3.13 .
Exercises are placed within the main body of the text to encourage active participation by the reader, with comprehensive solutions provided.Error Correcting Codes will appeal to undergraduate students in pure and applied mathematical ...
[1] Hill, R. (1986) A First Course in Coding Theory, Oxford University Press. [2] Wesley Peterson, W. (1962) ... [17] Vanstone, S.A. and van Oorschot, P.C.(1992) An Introduction to Error-correcting Codes with Applications, Kluwer.
Fundamentals of Error Correcting Codes is an in-depth introduction to coding theory from both an engineering and mathematical viewpoint.
This book starts by establishing the basic linear network error correction (LNEC) model and then characterizes two equivalent descriptions.
An introduction to the theory of error-correction codes, and in particular to linear block codes is provided in this book. It considers such codes as Hamming codes and Golay codes,...
5. 2 Rings and Ideals 148 5. 3 Ideals and Cyclic Subspaces 152 5. 4 Generator Matrices and Parity-Check Matrices 159 5. 5 Encoding Cyclic Codest 163 5. 6 Syndromes and Simple Decoding Procedures 168 5. 7 Burst Error Correcting 175 5. 8 ...
Because it carefully balances both theory and applications, this book will be an indispensable resource for readers seeking a timely treatment of error-correcting codes.
This book is open access under a CC BY 4.0 license. This book discusses both the theory and practical applications of self-correcting data, commonly known as error-correcting codes.
An introduction to the Nordstrom—Robinson code The extended Golay code '§2., may be used to construct some interesting nonlinear double-error-correcting codes. The construction. It will be convenient to change the order of the columns ...