03181nam 22006255 450 991014494060332120241010160058.03-540-45797-610.1007/b84213(CKB)1000000000233290(SSID)ssj0000321811(PQKBManifestationID)11255987(PQKBTitleCode)TC0000321811(PQKBWorkID)10279895(PQKB)11019537(DE-He213)978-3-540-45797-8(MiAaPQ)EBC6304228(MiAaPQ)EBC5585456(Au-PeEL)EBL5585456(OCoLC)1066177219(PPN)15522705X(EXLCZ)99100000000023329020121227d2002 u| 0engurnn#008mamaatxtccrCharacters and Cyclotomic Fields in Finite Geometry /by Bernhard Schmidt1st ed. 2002.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2002.1 online resource (VIII, 108 p.)Lecture Notes in Mathematics,0075-8434 ;1797Bibliographic Level Mode of Issuance: Monograph3-540-44243-X Includes bibliographical references and index.1. 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.This 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.Lecture Notes in Mathematics,0075-8434 ;1797Combinatorial analysisCombinatoricshttps://scigraph.springernature.com/ontologies/product-market-codes/M29010Combinatorial analysis.Combinatorics.516.1305B30msc05B10msc05B25mscSchmidt Bernhard1967-authttp://id.loc.gov/vocabulary/relators/aut1771472MiAaPQMiAaPQMiAaPQBOOK9910144940603321Characters and Cyclotomic Fields in Finite Geometry4261283UNINA