000 03532nam a22005295i 4500
001 978-3-540-28991-3
003 DE-He213
005 20161121231031.0
007 cr nn 008mamaa
008 100301s2006 gw | s |||| 0|eng d
020 _a9783540289913
_9978-3-540-28991-3
024 7 _a10.1007/3-540-28991-7
_2doi
050 4 _aQA164-167.2
072 7 _aPBV
_2bicssc
072 7 _aMAT036000
_2bisacsh
082 0 4 _a511.6
_223
100 1 _aKaski, Petteri.
_eauthor.
245 1 0 _aClassification Algorithms for Codes and Designs
_h[electronic resource] /
_cby Petteri Kaski, Patric R.J. Östergård.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2006.
300 _aXI, 412 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aAlgorithms and Computation in Mathematics,
_x1431-1550 ;
_v15
505 0 _aGraphs, Designs, and Codes -- Representations and Isomorphism -- Isomorph-Free Exhaustive Generation -- Auxiliary Algorithms -- Classification of Designs -- Classification of Codes -- Classification of Related Structures -- Prescribing Automorphism Groups -- Validity of Computational Results -- Computational Complexity -- Nonexistence of Projective Planes of Order 10.
520 _aA 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.
650 0 _aMathematics.
650 0 _aCoding theory.
650 0 _aComputer mathematics.
650 0 _aCombinatorics.
650 0 _aElectrical engineering.
650 1 4 _aMathematics.
650 2 4 _aCombinatorics.
650 2 4 _aComputational Mathematics and Numerical Analysis.
650 2 4 _aCoding and Information Theory.
650 2 4 _aCommunications Engineering, Networks.
650 2 4 _aSignal, Image and Speech Processing.
700 1 _aÖstergård, Patric R.J.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540289906
830 0 _aAlgorithms and Computation in Mathematics,
_x1431-1550 ;
_v15
856 4 0 _uhttp://dx.doi.org/10.1007/3-540-28991-7
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c507576
_d507576