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Correlation distribution of a sequence family generalizing some sequences of Trachtenberg

  • * Corresponding author: Eda Tekin

    * Corresponding author: Eda Tekin
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  • 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.

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