The main conjecture of this note is the following: if a cyclic (v = 4n - 1, k = 2n - 1, λ= n - 1) Hadmard difference set exists, the the value of v must be either a prime, or a product of “twin primes,” or one less than a power of 2. Six cases, v - 399, 495, 627, 651, 783, and 975, which were once listed as the possible exceptions for v < 1000, are now fully investigated, and all the cases of v < 10 000 are now verified relative to this conjecture, with at most 17 possible exceptions.
All Science Journal Classification (ASJC) codes
- Information Systems
- Computer Science Applications
- Library and Information Sciences