Some algebraic properties of finite binary sequences
Abstract
We study properties of differences of finite binary sequences with
a fixed number of ones. We show that any binary sequence consisting of $m$ terms (except of the sequence $(1, 0, \ldots, 0)$) can be presented as a difference of two sequences having exactly $n$ ones, whenever $\frac{1}{4} m < n < \frac{3}{4}m$.
a fixed number of ones. We show that any binary sequence consisting of $m$ terms (except of the sequence $(1, 0, \ldots, 0)$) can be presented as a difference of two sequences having exactly $n$ ones, whenever $\frac{1}{4} m < n < \frac{3}{4}m$.
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PDFDOI: https://doi.org/10.2478/tatra.v65i0.387