TY - BOOK ID - 6728809 TI - Characters and cyclotomic fields in finite geometry PY - 2002 VL - 1797 SN - 00758434 SN - 354044243X 3540457976 9783540442431 PB - Berlin Springer-Verlag DB - UniCat KW - Cyclotomy. KW - Difference sets. KW - Finite geometries. KW - Difference sets KW - Cyclotomy KW - Finite geometries KW - Algebra KW - Mathematical Theory KW - Mathematics KW - Physical Sciences & Mathematics KW - Combinatorics. KW - Combinatorics KW - Mathematical analysis UR - https://www.unicat.be/uniCat?func=search&query=sysid:6728809 AB - 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. ER -