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Let us lexicographically order the binary sequences of length by (3).
The ZCC (C, w) code is a family of binary sequences of length C and constant Hamming-weight w.
The distribution of cross-correlations is more complex, as there are no orthogonal binary sequences of length 4k + 2.
Later, set of binary sequences of length with autocorrelation sidelobes and cross-correlation peak values of approximately are studied in paper [4].
Given the amount of binary De Bruijn sequences obtainable, even for small values of the span parameter, and considering the great complexity of the generation process [13], we can provide an exhaustive analysis of binary sequences of length 32 (i.e., span 5) that form a set of 2,048 different sequences, and partial results for sequences generated by increasing values of the span.
On one hand, for aperiodic sequences, it is known that for most binary sequences of length the attainable sidelobe levels are approximately [2, 3] and the mutual peak cross-correlations of the same-length sequences are much larger and are usually in the order of to.
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Hence, the inheritance vector at site l, v l, can be defined as a binary sequence of length 2 × n.
More formally, we are given a dataset { (s i, y i ) } i = 1 n where s i is the binary sequence of length L representing the i-th individual and y i ∈ { Cases, Controls } is its corresponding binary phenotype.
We also obtained m(t), which is a pseudo random binary sequence of maximum-length (MLS or m-seq) presented at a rate of 40 Hz (i.e., 25 ms time interval) (2) m(t)={displaystyle {sum}_{m=0}^{M-1}{a}_mdelta left t-0.025mright left t-0.025mrightthe m-seq and M is the length of the sequence.
The set of all infinite binary sequences of outcomes is known as the Cantor space.
We study adaptation of a haploid asexual population on a fitness landscape defined over binary genotype sequences of length L. We consider greedy adaptive walks in which the population moves to the fittest among all single mutant neighbors of the current genotype until a local fitness maximum is reached.
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