21 problems

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

Nonexistence conjecture. No Barker sequences of length greater than $13$ exist.

Zhang–Zheng's conjecture. The absolute indicator of $f$ is at least

Schmidt's conjecture. There do not exist perfect binary sequences with

Nonexistence conjecture. There are no perfect binary sequences of period $N>4$.

Conjecture. The maximizing value $k_m^*$ is unique for every $m$, and

Let $N$ observations of a signal be collected from the model, with each observation sampled at $L$ equally spaced locations; let $M$ denote the number of grid points and let…

Let $C_4$ be the smallest constant such that … for the function class specified in Theorem 4 of the source. The compactly supported formulation concerns functions…

For $g\in L^1(\mathbb{R})$ with $g\geq 0$ and compact $I\subset\mathbb{R}$, let $\mathcal{L}_g(I)$ be the class of nonnegative $L^1$ functions $f$ on $\mathbb{R}$ such that…

The discussion concerns statistical tests for linear dependence between time series, including prewhitening, Granger causality, and $F$- or $\chi^2$-tests; autocorrelation in the u…

Zero-correlation condition conjecture. The condition that the state space is $\{-N,-N+1,\ldots,-1,+1,+2,\ldots,+N\}$ and the equilibrium distribution is uniform is necessary for…

Uniqueness conjecture. The only perfect sequence is the sequence with $N=4$ and $S=(0,0,0,1,\ldots)$, up to cyclic-shift equivalence.

For a binary sequence $X$ of length $n$, write $PComS(n,q,c)$ for the family used in the paper, and let a perfect binary sequence have two-level nontrivial autocorrelation with val…

A binary sequence is a sequence with entries in $\{+1,-1\}$. Its autocorrelation merit factor is the reciprocal of its autocorrelation demerit factor, and the asymptotic merit fact…

A binary sequence is a sequence with entries in $\{+1,-1\}$. Its autocorrelation demerit factor measures the normalized total squared contribution of its nonzero aperiodic autocorr…

Let $B$ be the intersection indicator observable for a concatenated pair of self-avoiding walks of total length $N$, and let $\tau_{\mathrm{int}}(B)$ denote its integrated autocorr…

Let $s$ and $e$ be random elements respectively of $S_N$ and $E_N$, and let $n(x)=s(x)s(1/x)+e(x)$ be the corresponding noisy autocorrelation. The preceding theorem gives the proba…

Let $\mathcal{B}_n$ be the set of all binary sequences of length $n$, and let $\mu(A)$ denote the peak sidelobe level of $A\in\mathcal{B}_n$. An infinite family means sequences of…

A Barker sequence is a binary sequence for which every nontrivial aperiodic autocorrelation has magnitude at most $1$. Turyn's conjecture. There is no Barker sequence of length gre…

Lin's conjecture. The sequence $S$ has ideal two-level autocorrelation; that is, if its period is $N$, then

Let $a_1,\ldots,a_n$ be a Barker sequence: each $a_i\in\{\pm1\}$ and its aperiodic autocorrelations $c_k=\sum_{i=1}^{n-k}a_i a_{i+k}$ satisfy $|c_k|\leq1$ for every $k\geq1$. Barke…