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Handbook of coding theory. Vol. 1. Part 1: Algebraic coding. Vol. 2. Part 2: Connections, Part 3: Applications. (English) Zbl 0907.94001
Amsterdam: Elsevier. 2169 p. (1998).

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This is an extraordinary collection of survey articles to almost all aspects of coding theory written by experts in the field. We cite from the introduction: “The Handbook is divided into three parts, the first part comprising Volume I and the remaining two parts Volume II. Part 1, Algebraic Coding, deals primarily with the algebraic structure of error correcting codes. Part 2, Connections, is devoted to connections between coding theory and other branches of mathematics and computer science. Part 3, Applications, deals with a variety of applications of coding. The authors have taken a broad perspective on their topics, and, by interacting with other authors, have often established links between the chapters. Most of the chapters are self-contained with the majority of the proofs presented in full. Open problems are often identified, and many chapters bring the reader to the frontiers of research. Each chapter provides an extensive bibliography that will be a tool to extend the development of that chapter.”
It is definitely a must for every library.
The articles of this volume will be reviewed individually.
Indexed articles:
Pless, Vera S.; Huffman, W. Cary; Brualdi, Richard A., An introduction to algebraic codes, 3-139 [Zbl 0919.94049]
Pless, Vera, Coding constructions, 141-176 [Zbl 0924.94037]
Rains, Eric M.; Sloane, N. J. A., Self-dual codes, 177-294 [Zbl 0936.94017]
Brouwer, A. E., Bounds on the size of linear codes, 295-461 [Zbl 0936.94015]
Litsyn, Simon, An updated table of the best binary codes known, 463-498 [Zbl 0968.94019]
Levenshtein, Vladimir I., Universal bounds for codes and designs, 499-648 [Zbl 0983.94056]
Barg, Alexander, Complexity issues in coding theory, 649-754 [Zbl 0929.94028]
Brualdi, Richard A.; Litsyn, Simon; Pless, Vera S., Covering radius, 755-826 [Zbl 0922.94020]
Ward, Harold N., Quadratic residue codes and divisibility, 827-870 [Zbl 0922.94012]
Høholdt, Tom; van Lint, Jacobus H.; Pellikaan, Ruud, Algebraic geometry codes, 871-961 [Zbl 0922.94015]
Charpin, Pascale, Open problems on cyclic codes, 963-1063 [Zbl 0927.94017]
McEliece, Robert J., The algebraic theory of convolutional codes, 1065-1138 [Zbl 0967.94020]
Honkala, Iiro; Tietäväinen, Aimo, Codes and number theory, 1141-1194 [Zbl 0929.94032]
van Tilborg, Henk C. A., Coding theory at work in cryptology and vice versa, 1195-1227 [Zbl 0967.94010]
Tonchev, Vladimir D., Codes and designs, 1229-1267 [Zbl 0922.94011]
Assmus, E. F. jun.; Key, J. D., Polynomial codes and finite geometries, 1269-1343 [Zbl 0980.94038]
Huffman, W. Cary, Codes and groups, 1345-1440 [Zbl 0926.94039]
Camion, Paul, Codes and association schemes: Basic properties of association schemes relevant to coding, 1441-1566 [Zbl 0978.94048]
Blahut, Richard E., Decoding of cyclic codes and codes on curves, 1569-1633 [Zbl 0922.94018]
Marcus, Brian H.; Roth, Ron M.; Siegel, Paul H., Constrained systems and coding for recording channels, 1635-1764 [Zbl 0983.94015]
Helleseth, Tor; Kumar, P. Vijay, Sequences with low correlation, 1765-1853 [Zbl 0924.94027]
Blaum, Mario; Farrell, Patrick G.; van Tilborg, Henk C. A., Array codes, 1855-1909 [Zbl 0978.94044]
Dumer, Ilya I., Concatenated codes and their multilevel generalizations, 1911-1988 [Zbl 0967.94029]
Vardy, Alexander, Trellis structure of codes, 1989-2117 [Zbl 0922.94013]
Wicker, Stephen B., Deep space applications, 2119-2169 [Zbl 0978.94049]

94-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to information and communication theory
00B15 Collections of articles of miscellaneous specific interest
94-06 Proceedings, conferences, collections, etc. pertaining to information and communication theory