A first course in coding theory.

*(English)*Zbl 0616.94006
Oxford Applied Mathematics and Computing Science Series. Oxford: Clarendon Press. XII, 251 p. (1986).

From the preface of the book: ”The aim of this book is to provide an elementary treatment of the theory of error correcting codes, assuming no more than high school mathematics and the ability to carry out matrix arithmetic. The book is intended to serve as a self contained course for second or third year mathematics undergraduates, or as a readable introduction to the mathematical aspects of coding for students in engineering or computer science.” In these goals the book is eminently successful. It is perhaps closest in spirit and level to the book by V. Pless [Introduction to the theory of error correcting codes (1981; Zbl 0481.94004)] with perhaps a more uniform coverage of block coding theory and random error correction and less emphasis on quadratic codes and t-designs than the Pless book. For much of the book only prime fields are used, to accommodate the desire to keep it readable by a wide audience, but virtually all of the important basic results of coding are covered at a useful level. A feature of the book is an abundant selection of interesting problems with the solutions provided at the end of the book. This includes chapters on encoding and decoding linear codes, the dual code, the parity check matrix and syndrome decoding, Hamming codes, perfect codes, codes and latin squares, BCH codes, weight enumerators and the probability of undetected errors, maximum distance separable codes and a chapter on the ”main linear coding theory” problem (for a given code length, find the maximum dimension k such that there exists an (n,k,d) code). Extension fields are covered as cyclic codes are introduced in chapter 12. The book, as designed, would serve admirably as a text for an undergraduate course in coding in computer science, mathematics or engineering.

Reviewer: I.F.Blake

##### MSC:

94B05 | Linear codes, general |

94-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory |