000 | 02771nam a22004575i 4500 | ||
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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 |
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024 | 7 |
_a10.1007/b84213 _2doi |
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050 | 4 | _aQA164-167.2 | |
072 | 7 |
_aPBV _2bicssc |
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072 | 7 |
_aMAT036000 _2bisacsh |
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072 | 7 |
_aPBV _2thema |
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082 | 0 | 4 |
_a511.6 _223 |
100 | 1 |
_aSchmidt, Bernhard. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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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. |
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300 |
_aVIII, 108 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1797 |
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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 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/b84213 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
912 | _aZDB-2-BAE | ||
999 |
_c9688 _d9688 |