6 problems

Let $G_1$ and $G_2$ be groups, and let a circular Costas map be a map $\varphi:G_1\to G_2$ that is injective and whose nonzero difference maps are injective; call it standard when…

Let $\mathbb{Z}_n$ denote the cyclic group of order $n$. A circular Costas sequence is equivalent to an injective map $\varphi:\mathbb{Z}_n\to\mathbb{Z}_{n+1}$ whose difference map…

Let a Costas sequence be a sequence whose difference triangle has no repeated entry in any row. A sequence is singly periodical when every circular shift of its terms is also a Cos…

Higher-dimensional periodic Costas array conjecture. If $A$ is periodic Costas, then $n=2^k$. In particular,

W1–G2 cross-correlation conjecture.

G2 cross-correlation conjecture.