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DCG
2011
12 years 11 months ago
New Classes of Counterexamples to Hendrickson's Global Rigidity Conjecture
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...
Samuel Frank, Jiayang Jiang
DCG
2011
12 years 11 months ago
More Colourful Simplices
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 ...
Antoine Deza, Tamon Stephen, Feng Xie
DCG
2011
12 years 11 months ago
Lines Pinning Lines
Boris Aronov, Otfried Cheong, Xavier Goaoc, Gü...
DCG
2011
12 years 11 months ago
Random Geometric Complexes
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...
Matthew Kahle
DCC
2011
IEEE
12 years 11 months ago
Some observations on HC-128
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...
Subhamoy Maitra, Goutam Paul, Shashwat Raizada, Su...
DCC
2011
IEEE
12 years 11 months ago
On the correlation distribution of Delsarte-Goethals sequences
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...
Kai-Uwe Schmidt
DCC
2011
IEEE
12 years 11 months ago
Quaternary Golay sequence pairs II: odd length
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...
Richard G. Gibson, Jonathan Jedwab
DCC
2011
IEEE
12 years 11 months ago
Directed graph representation of half-rate additive codes over GF(4)
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 ...
Lars Eirik Danielsen, Matthew G. Parker