IEICE Transactions on Communications
Online ISSN : 1745-1345
Print ISSN : 0916-8516
Regular Section
A Proof of Turyn's Conjecture: Nonexistence of Circulant Hadamard Matrices for Order Greater than Four
Yoshimasa OH-HASHI
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2016 Volume E99.B Issue 7 Pages 1395-1407

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Abstract

Biphase periodic sequences having elements +1 or -1 with the two-level autocorrelation function are desirable in communications and radars. However, in case of the biphase orthogonal periodic sequences, Turyn has conjectured that there exist only sequences with period 4, i.e., there exist the circulant Hadamard matrices for order 4 only. In this paper, it is described that the conjecture is proved to be true by means of the isomorphic mapping, the Chinese remainder theorem, the linear algebra, etc.

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© 2016 The Institute of Electronics, Information and Communication Engineers
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