### Abstract

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 language | English |
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Pages (from-to) | 1266-1268 |

Number of pages | 3 |

Journal | IEEE Transactions on Information Theory |

Volume | 40 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1994 Jul |

### All Science Journal Classification (ASJC) codes

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

## Cite this

Song, H. Y., & Golomb, S. W. (1994). On the Existence of Cyclic Hadamard Difference Sets.

*IEEE Transactions on Information Theory*,*40*(4), 1266-1268. https://doi.org/10.1109/18.335939