17 problems

Helleseth's vanishing conjecture. If $q>2$ and $s\equiv 1 \pmod{p-1}$, then $s$ is singular.

Berggren–Popović's conjecture. All normalized QPP-interleaved Zadoff–Chu sequences are inequivalent to ordinary Zadoff–Chu sequences precisely when

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…

Turyn's conjecture. No BGCPs exist for any length $M$ not of the form $2^a10^b26^c$ with $a,b,c\geq0$.

Let a quasi-complementary sequence set (QCSS) have set size $M$, flock size $K$, sequence length $N$, and tightness factor $\rho$. It is asymptotically near-optimal when its correl…

Let $\mathcal{S}$ be an $(N,L,Z)$-ZCZ sequence set, meaning a set of $N$ complex sequences of length $L$ whose auto- and cross-correlation values vanish in the specified zero-corre…

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…

Uniqueness conjecture. Only unique sequences are obtained when

Let $\boldsymbol{\mathscr{Z}}$ be a $(K,Z,L)$-ZCZ sequence set, and let its performance parameter be … For binary ZCZ sequence sets, the binary performance-parameter conjecture. ……

Non-existence conjecture. Let $m\geq 5$ be a prime, $\gamma_1,\gamma_2\in\mathbb Z$, and $n\in\mathbb Z^+$. There does not exist a non-trivial almost $m$-ary NPS of type…

A binary Barker sequence is a binary sequence whose aperiodic autocorrelation sidelobes have magnitude at most $1$. Barker sequence nonexistence conjecture. No binary Barker sequen…

Let a binary Z-complementary pair (ZCP) consist of two binary sequences of even length $L$, where … The zero-correlation-zone (ZCZ) width $Z$ is the width within which the pair 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,…

Approximation-ratio conjecture. The ratio satisfies

Let $\mathcal{L}=\bigcup_{N=1}^{+\infty}\{+1,-1\}^N$ be the class of Littlewood sequences, and let $U_N(z)$ denote the associated $L^2$-normalized analytic polynomial for a sequenc…

Characterization conjecture. All three-valued cross correlations between two $m$-sequences of lengths $2^m-1$ and $2^{m/2}-1$ are characterized.

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