### 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 Jan 1 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*IEEE Transactions on Information Theory*,

*40*(4), 1266-1268. https://doi.org/10.1109/18.335939

}

*IEEE Transactions on Information Theory*, vol. 40, no. 4, pp. 1266-1268. https://doi.org/10.1109/18.335939

**On the Existence of Cyclic Hadamard Difference Sets.** / Song, Hong-Yeop; Golomb, Solomon W.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the Existence of Cyclic Hadamard Difference Sets

AU - Song, Hong-Yeop

AU - Golomb, Solomon W.

PY - 1994/1/1

Y1 - 1994/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0028462460&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028462460&partnerID=8YFLogxK

U2 - 10.1109/18.335939

DO - 10.1109/18.335939

M3 - Article

AN - SCOPUS:0028462460

VL - 40

SP - 1266

EP - 1268

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 4

ER -