Correlation distribution of a sequence family generalizing some sequences of Trachtenberg

Abstract

In this paper, we give a classification of a sequence family, over arbitrary characteristic, adding linear trace terms to the function g(x) = 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 (τ ) ∈ {−1, −1 ± p n+e 2 , −1 + p n }.