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We examine the generic local and global rigidity of various graphs in Rd . Bruce Hendrickson showed that some necessary conditions for generic global rigidity are (d + 1)-connected...
We show that any point in the convex hull of each of (d +1) sets of (d +1) points in general position in Rd is contained in at least (d + 1)2/2 simplices with one vertex from each ...
We study the expected topological properties of ˇCech and Vietoris-Rips complexes built on random points in Rd . We find higher dimensional analogues of known results for connect...
In this paper, we use linear approximations of the addition modulo 2n of three n-bit integers to identify linear approximations of g1, g2, the feedback functions of HC-128. This, i...
For odd integer m ≥ 3 and t = 0, 1, . . . , m−1 2 , we define Family V (t) to be a set of size 2m(t+1) containing binary sequences of period 2m+1 − 2. The nontrivial correl...
A 4-phase Golay sequence pair of length s ≡ 5 (mod 8) is constructed from a Barker sequence of the same length whose even-indexed elements are prescribed. This explains the orig...
We show that (n, 2n ) additive codes over GF(4) can be represented as directed graphs. This generalizes earlier results on self-dual additive codes over GF(4), which correspond to ...