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Introduction to coding theory. 3rd rev. and exp. ed. (English) Zbl 0936.94014
Graduate Texts in Mathematics. 86. Berlin: Springer. xiv, 227 p. (1999).
Over the past decades many books on coding theory have been issued but ”Introduction to Coding Theory” by J. H. van Lint remains to be one of the most favorite textbooks for many lecturers giving courses on coding theory. So the appearance of the 3rd edition is a very welcome event.
Here we point out only the revisions and expansions and refer to “Coding theory”, Lect. Notes Math. 201 (1971; Zbl 0224.94002), and previous eds. (1st ed. 1982; Zbl 0485.94015 and 2nd ed. 1992; Zbl 0747.94018) for more information.
The main additions are:
(1) Two new chapters: “Codes over \(\mathbb Z_4\)” and “Algebraic geometry codes”, are added. The corresponding research areas are currently enjoying strong interest and fast development. Both chapters are supplied with plenty of examples and exercises. Each of them is a brief, but lucid introduction to the subject providing the reader with the necessary knowledge for further studying.
(2) Chapter 6 “Cyclic codes” is expanded by including Generalized Reed-Solomon codes and Generalized Reed-Muller codes. Also, a paragraph (“Coding gains”) concerning more practical aspects of using error-correcting codes is added in Chapter 2. The section “The Lee metric” is another addition.

94Bxx Theory of error-correcting codes and error-detecting codes
94-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory
94B05 Linear codes, general
94A20 Sampling theory in information and communication theory
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
94B10 Convolutional codes
94B15 Cyclic codes
94B27 Geometric methods (including applications of algebraic geometry) applied to coding theory
94B40 Arithmetic codes