On the joint 2-adic complexity of binary multisequences (Q2905327)

In [\textit{M. Goresky} et al., IEEE Trans. Inf. Theory 46, No. 2, 687--691 (2000; Zbl 0996.94029)] the 2-adic complexity of a binary sequence has been related to the number of nonzero classical Fourier coefficients of the sequence. In this article the authors adapt the Fourier transform in the obvious way for multisequences, and convert the upper bound for the 2-adic complexity given in [loc. cit.] to the corresponding bound for the joint 2-adic complexity of a multisequence. Using the known relations between Fourier coefficients, it is pointed out in Theorem 3.5 that the bounds can be expressed using the factorization of the period length \(L\) (\(L\) odd) of the sequence. (The formulation of the theorem is misleading, differently than claimed an upper bound is not given there, solely the shape of the bound in Theorem 3.3 is explained.) The paper finishes with a description of an upper bound for the number of \(p^n\)-periodic multisequences with given joint 2-adic complexity, \(p>2\) prime.