On the Existence of Cyclic Hadamard Difference Sets

Hong Y. Song; Solomon W. Golomb

doi:10.1109/18.335939

On the Existence of Cyclic Hadamard Difference Sets

Hong Y. Song, Solomon W. Golomb

Department of Electrical and Electronic Engineering

Research output: Contribution to journal › Article › peer-review

35 Citations (Scopus)

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
Pages (from-to)	1266-1268
Number of pages	3
Journal	IEEE Transactions on Information Theory
Volume	40
Issue number	4
DOIs	https://doi.org/10.1109/18.335939
Publication status	Published - 1994 Jul

All Science Journal Classification (ASJC) codes

Information Systems
Computer Science Applications
Library and Information Sciences

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10.1109/18.335939

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On the Existence of Cyclic Hadamard Difference Sets

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