On the Existence of Cyclic Hadamard Difference Sets

Hong Y. Song, Solomon W. Golomb

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1266-1268
Number of pages3
JournalIEEE Transactions on Information Theory
Issue number4
Publication statusPublished - 1994 Jul

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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