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On the existence of cyclic Hadamard difference sets

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2 Author(s)
Song, H.Y. ; Dept. of Electr. Eng. Syst., Univ. of Southern California, Los Angeles, CA, USA ; Golomb, S.W.

The main conjecture of this article is the following: if a cyclic (v=4n-1, k=2n-1, λ=n-1) Hadamard 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<10000 are now verified relative to this conjecture, with at most 17 possible exceptions

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Information Theory, IEEE Transactions on  (Volume:40 ,  Issue: 4 )