000 02771nam a22004575i 4500
001 978-3-540-45797-8
003 DE-He213
005 20190213151140.0
007 cr nn 008mamaa
008 121227s2002 gw | s |||| 0|eng d
020 _a9783540457978
_9978-3-540-45797-8
024 7 _a10.1007/b84213
_2doi
050 4 _aQA164-167.2
072 7 _aPBV
_2bicssc
072 7 _aMAT036000
_2bisacsh
072 7 _aPBV
_2thema
082 0 4 _a511.6
_223
100 1 _aSchmidt, Bernhard.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aCharacters and Cyclotomic Fields in Finite Geometry
_h[electronic resource] /
_cby Bernhard Schmidt.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2002.
300 _aVIII, 108 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1797
505 0 _a1. Introduction: The nature of the problems -- The combinatorial structures in question -- Group rings, characters, Fourier analysis -- Number theoretic tools -- Algebraic-combinatorial tools. 2. The field descent: The fixing theorem -- Prescribed absolute value -- Bounding the absoute value -- The modulus equation and the class group. 3. Exponent bounds: Self-conjugacy exponent bounds -- Field descent exponent bounds. 4. Two-weight irreducible cyclic bounds: A necessary and sufficient condition -- All two-weight irreducible cyclic codes?- Partial proof of Conjecture 4.2.4 -- Two-intersection sets and sub-difference sets.
520 _aThis monograph contributes to the existence theory of difference sets, cyclic irreducible codes and similar objects. The new method of field descent for cyclotomic integers of presribed absolute value is developed. Applications include the first substantial progress towards the Circulant Hadamard Matrix Conjecture and Ryser`s conjecture since decades. It is shown that there is no Barker sequence of length l with 13<1<4x10^(12). Finally, a conjecturally complete classification of all irreducible cyclic two-weight codes is obtained.
650 0 _aCombinatorics.
650 1 4 _aCombinatorics.
_0http://scigraph.springernature.com/things/product-market-codes/M29010
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540442431
776 0 8 _iPrinted edition:
_z9783662183199
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1797
856 4 0 _uhttps://doi.org/10.1007/b84213
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c9688
_d9688