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100   $a20121227d2002      u|             0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aCharacters and Cyclotomic Fields in Finite Geometry$b[electronic resource] /$fby Bernhard Schmidt
205   $a1st ed. 2002.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2002.
215   $a1 online resource (VIII, 108 p.)
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1797
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-540-44243-X 
320   $aIncludes bibliographical references and index.
327   $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.
330   $aThis monograph contributes to the existence theory of difference sets, cyclic irreducible codes and similar objects. The new method of field descent for cyclotomic integers of presribed absolute value is developed. Applications include the first substantial progress towards the Circulant Hadamard Matrix Conjecture and Ryser`s conjecture since decades. It is shown that there is no Barker sequence of length l with 13<1<4x10^(12). Finally, a conjecturally complete classification of all irreducible cyclic two-weight codes is obtained.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1797
606   $aCombinatorics
606   $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010
615  0$aCombinatorics.
615 14$aCombinatorics.
676   $a516.13
686   $a05B30$2msc
686   $a05B10$2msc
686   $a05B25$2msc
700   $aSchmidt$b Bernhard$4aut$4http://id.loc.gov/vocabulary/relators/aut$0352587
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910144940603321
996   $aCharacters and cyclotomic fields in finite geometry$9262253
997   $aUNINA