Correlation distribution of a sequence family generalizing some sequences of trachtenberg

2021-08-01
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)}.
ADVANCES IN MATHEMATICS OF COMMUNICATIONS

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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: https://hdl.handle.net/11511/92015.