8 problems

A binary sequence $f$ has merit factor $\operatorname{MF}(f)$, and its asymptotic merit factor is the limiting value of $\operatorname{MF}(f)$ as the length of $f$ tends to infinit…

Bernasconi's conjecture. Stochastic search procedures will not yield merit factors higher than $5$ for long sequences.

Stochastic-search merit-factor conjecture. Stochastic search procedures will not yield merit factors higher than $5$ for long binary sequences.

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 $q$ be an odd prime power, let $\theta$ be primitive in $\mathbb{F}_q$, and let $Z_{n,\theta}$ be the Sidelnikov sequence of length $n=q-1$ with respect to $\theta$. Let $F$ de…

Let $F=\mathbb{F}_{2^d}$ and let $K$ be a subfield of size $2^k$, where $k$ divides $d$. Let $\theta$ be primitive in $F$, let $\ell$ be coprime to $2^k-1$, and let the Gordon-Mill…

Let $A$ be a sequence obtained by appending an initial fraction of a rotated Legendre sequence to itself. Borwein et al.'s conjecture. This sequence family has asymptotic merit fac…