6 problems

Let $H\in\{\pm1\}^{n\times n}$ be a circulant Hadamard matrix, equivalently a perfect binary sequence of length $n$. The length-$4$ sequence $[1,-1,-1,-1]$ is the only nontrivial p…

Mow's conjecture. No perfect periodic autocorrelation sequence over an $n$-phase alphabet can have length

A polyphase sequence is a sequence whose elements are complex roots of unity of the form $\exp(i2\pi x)$, where $x$ is rational and $i=\sqrt{-1}$. A perfect polyphase sequence has…

Let an odd perfect sequence be a sequence whose relevant periodic autocorrelations vanish at odd shifts, and consider sequences over the alphabet $\{\pm1,\pm i\}$. Lüke, Schotten,…

A perfect sequence is a sequence whose nontrivial periodic autocorrelations vanish. The alphabet of a sequence is the set of symbols from which its entries are drawn; here the alph…

Length-64 conjecture. The longest perfect sequence over the simple unit quaternions with the AOP is of length $64$. This conjecture is motivated by an exhaustive random search that…