Correlation distribution of a sequence family generalizing some sequences of trachtenberg

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,C-j(tau) is an element of {-1, -1 +/- p(n+e/2), -1 + p(n)}.


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In this paper a new binary sequence family with 2(n) + 1 cyclically distinct sequences each having length 2(n) - 1 is presented for an even integer n. The correlation distribution of the family is fully determined. The family has six-valued correlation distribution and its maximum correlation magnitude equals 1 + 2(n/2 + 1).
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We obtain concrete upper bounds on the algebraic immunity of a class of highly nonlinear plateaued functions without linear structures than the one was given recently in 2017, Cusick. Moreover, we extend Cusick’s class to a much bigger explicit class and we show that our class has better algebraic immunity by an explicit example. We also give a new notion of linear translator, which includes the Frobenius linear translator given in 2018, Cepak, Pasalic and Muratović-Ribić as a special case. We find some app...
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Citation Formats
F. Özbudak, “Correlation distribution of a sequence family generalizing some sequences of trachtenberg,” ADVANCES IN MATHEMATICS OF COMMUNICATIONS, vol. 15, no. 4, pp. 647–662, 2021, Accessed: 00, 2021. [Online]. Available: