Classification Algorithms for Codes and Designs

Kirjan Classification Algorithms for Codes and Designs (2005) on kirjoittanut Petteri Kaski. Kirjan kieli on englanti, ja sen on kustantanut Springer-Verlag Berlin and Heidelberg GmbH Co. K. Kirja on laajuudeltaan 412 sivua ja se on sidottu.

A new starting-point and a new method are requisite, to insure a complete [classi? cation of the Steiner triple systems of order 15]. This method was furnished, and its tedious and di? cult execution und- taken, by Mr. Cole. F. N. Cole, L. D. Cummings, and H. S. White (1917) [129] The history of classifying combinatorial objects is as old as the history of the objects themselves. In the mid-19th century, Kirkman, Steiner, and others became the fathers of modern combinatorics, and their work – on various objects, including (what became later known as) Steiner triple systems – led to several classi? cation results. Almost a century earlier, in 1782, Euler [180] published some results on classifying small Latin squares, but for the ? rst few steps in this direction one should actually go at least as far back as ancient Greece and the proof that there are exactly ? ve Platonic solids. One of the most 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 arguments are e? ective (often to prove nonexistence or uniqueness), classi? cation in general is about algorithms and computation.