Classification Algorithms for Codes and Designs (Petteri Kaski and Patric R.J. Östergård; Springer Verlag, 2006)

From constrains to classes

Kaski and Östergård, two researchers from TKK (Helsinki University of Technology), have written a reference on classification of combinatorial objects. The book can be also used on advanced courses in computer science or mathematics.

The book is written in a concise and formal style, emphasizing the results and to some degree downplaying the pedagogical aspects. The book is challenging if the reader is not already acquainted with the field. But the algorithms and results included in the book provide a concise and useful reference for researchers.

The book is cross-disciplinary, and combines aspects of mathematics and computer science. The style of the exposition varies a bit from chapter to chapter, ranging from a terse mathematical style to a more verbose explanatory style.

Some of the figures illustrating the theorems and definitions seem afterthoughts, and may not clarify the matter due to short captions and explanations in the text. Many of these figures are quite suitable to be used on the blackboard, but a bit more verbose style would help the reader. On the other hand, it is not necessarily a bad thing that the reader has to do some thinking by himself.

Terminology poses problems in a book like this because many terms are used differently within the different fields. Understanding the definitions used in the book takes some time. On the other hand, the book can be used in manual style, starting from a chapter discussing the topic of interest, and looking up the definitions on the go.

The book contains an extensive bibliography and a useful index. The included DVD contains a catalogue of combinatorial objects.

Petteri Kaski was awarded the Dissertation of the Year prize in February 2006 by TKK for his Ph.D. thesis "Algorithms for Classification of Combinatorial Objects". In the thesis, Kaski solved the classification problem of Steiner triple systems of order 19. The previous result was 90 years old, and applied to order 15 systems.