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Article Contents

# Correlation distribution of a sequence family generalizing some sequences of Trachtenberg

• * Corresponding author: Eda Tekin
• In this paper, we give a classification of a sequence family, over arbitrary characteristic, adding linear trace terms to the function $g(x) = \mathrm{Tr}(x^d)$, where $d = p^{2k}-p^k+1$, first introduced by Trachtenberg. The family has $p^n+1$ cyclically distinct sequences with period $p^n-1$. We compute the exact correlation distribution of the function $g(x)$ with linear $m$-sequences and amongst themselves. The cross-correlation values are obtained as $C_{i,j}(\tau) \in \{-1,-1\pm p^{\frac{n+e}{2}},-1+p^n\}$.

Mathematics Subject Classification: Primary: 94A55, 11T71; Secondary: 14G50.

 Citation:

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