On the existence of cyclic hadamard difference sets

摘要

Every known cyclic Hadamard difference sets have one of the three types of v: (1) v=4n-1 is a prime. (2) v is a product of twin primes. (3) v=2~n-1 for n=2,3,.... It is conjectured that all the cyclic Hadamard difference sets have parameter v which falls into one of the three types. The conjecture has been previously confirmed for n <10000 except for 17 cases not fully investigated. In this paper, four smallest cases among these 17 cases are examined and confirmed the conjecture for all v<=3435.