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In this paper, we show that the d-decimation of a Sidelnikov sequence is the d-multiple of another Sidelnikov sequence and vice versa. Also, we calculate the crosscorrelation magnitude between d- and d′-decimations of a Sidelnikov sequence of period q − 1 to be upper bounded by (d+d′ − 1) √q+3.
The mathematical backbone of this article is formed by three classical formulas of Wallis: his product formula for π, an inequality implying the product formula in the limit, and a related definite integral involving powers of the sine function. For the latter we present various evaluations to illustrate recent algorithmic developments. In the main part of the article we automatically refine...
We propose a built-in scheme for generating all patterns of a given deterministic test set T. The scheme is based on grouping the columns of T, so that in each group of columns the number ri of unique representatives (row subvectors) as well as their product R over all such groups is kept at a minimum. The representatives of each group (segment) are then generated by a small finite state machine (FSM)...
Let d = d(n) be the minimum d such that for every sequence of n subsets F1, F2, . . . , Fn of {1, 2, . . . , n} there exist n points P1, P2, . . . , Pn and n hyperplanes H1, H2 .... , Hn in Rd such that Pj lies in the positive side of Hi iff j ∈ Fi. Then n/32 ≤ d(n) ≤ (1/2 + 0(1)) ?? n. This implies that the probabilistic unbounded-error 2-way complexity of almost all the Boolean functions of 2p variables...
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