Dan wrote:
The paper (Determinants of binary circulant matrices. Proceedings of the ISIT, 2004) appears to discuss this question, but it requires a subscription or download fee.
< http://ieeexplore.ieee.org/Xplore/login.jsp?url=/iel5/9423/29909/01365161.pd...
The "extended version", i.e. the one which actually contains proofs, is at http://www.math.unizh.ch/user/gmaze/Articles/detcirc2.pdf This paper explores the question of whether a circulant matrix whose entries are all {0,1} or all {-1,1} can have as large a determinant as is possible if you remove the "circulant" criterion (a.k.a. the Hadamard bound). I don't think it answers Fred's determinant question, but I just skimmed it. --Michael Kleber
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Many references to this question mention "Hadamard bounds" or "Gram-Hadamard bounds" -- whatever that means -- on the size of a determinant.
--Dan
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