Titlebook: Classification Algorithms for Codes and Designs; Petteri Kaski,Patric R.J. Östergård Book 2006 Springer-Verlag Berlin Heidelberg 2006 algo

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Graphs, Designs, and Codes,This chapter gives a brief introduction to graphs, designs, codes, and concepts related to these. Although classification algorithms for graphs are not considered in this book, graphs provide a convenient framework for several of the concepts and algorithms to be discussed.

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Classification of Codes,In this chapter, classification of several main classes of codes are considered: unrestricted error-correcting and covering codes in Sects. 7.1 and 7.2, respectively, and error-correcting linear codes in Sect. 7.3. Various subclasses of these codes are also discussed, including equidistant codes and constant weight codes.

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Book 2006most remarkable achievements in the early, pre-computer era is the classi?cation of the Steiner triple systems of order 15, quoted above. An onerous task that, today, no sensible person would attempt by hand calcu- tion. Because, with the exception of occasional parameters for which com- natorial ar

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Classification of Designs,alanced incomplete block designs (BIBDs) – that is, 2-designs – are considered in Sect. 6.1, .-designs with . ≥ 3 in Sect. 6.2, and resolutions of designs in Sect. 6.3. In the discussion of resolutions of designs, the main focus is on resolutions of BIBDs. Extensive tables of classification results

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Prescribing Automorphism Groups,a subfamily of these with certain additional properties. There are two possibilities for carrying out such a classification, which we have already encountered in discussing classification algorithms for resolutions of designs in Sect. 6.3: either all objects are classified and these are searched for