Zibi Xiao

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20182021

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math.NT2021

Binary Sequences Derived from Differences of Consecutive Primitive Roots

Arne Winterhof, Zibi Xiao

Let $1 < g_{1} < \dots < g_{φ (p - 1)} < p - 1$ be the ordered primitive roots modulo~ $p$ . We study the pseudorandomness of the binary sequence $(s_{n})$ defined by $s_n\equiv g_{n+1}+g_{n+2}\bmod…

math.NT2020

Binary sequences derived from differences of consecutive quadratic residues

Arne Winterhof, Zibi Xiao

For a prime $p \geq 5$ let $q_{0}, q_{1}, \dots, q_{(p - 3) /2}$ be the quadratic residues modulo $p$ in increasing order. We study two $(p - 3) /2$ -periodic binary sequences $(d_{n})$ and $(t_{n})$ …