A practical algorithm for completing half-Hadamard matrices using LLL

Journal of Algebraic Combinatorics - A (classical) partial Hadamard Matrix is an $$m\times n$$ matrix H with values in $$\{-1,1\}$$ such that $$HH^T=nI_m$$ . If $$m=n$$ , we say that H is a (full)...     

Study of proper circulant weighing matrices with weight 9

We provide the first theoretical proof of the spectrum of orders n for which circulant weighing matrices with weight 9 exist. This spectrum consists of those positive integers n, which are multiples of 13 or 24. We actually characterize the “minimal” examples which exist for orders 13, 26, or 24.     

Discovering the Higgs through highly-displaced vertices

We suggest that the Higgs could be discovered at the Tevatron or the LHC (perhaps at the LHCb detector) through decays with one or more substantially displaced vertices from the decay of new neutral particles. This signal may occur with a small but measurable branching fraction in the recently-described “hidden valley” models, hep-ph/0604261; weakly-coupled models with multiple scalars, including those of hep-ph/0511250, can also provide such signals, potentially with a much larger branching fraction. This decay channel may extend the Higgs mass reach for the Tevatron. Unusual combinations of b jets, lepton pairs and/or missing energy may accompany this signal.