1. CJM 2005 (vol 57 pp. 338)
 Lange, Tanja; Shparlinski, Igor E.

Certain Exponential Sums and Random Walks on Elliptic Curves
For a given elliptic curve $\E$, we obtain an upper bound
on the discrepancy of sets of
multiples $z_sG$ where $z_s$ runs through a sequence
$\cZ=\(z_1, \dots, z_T\)$
such that $k z_1,\dots, kz_T $ is a permutation of
$z_1, \dots, z_T$, both sequences taken modulo $t$, for
sufficiently many distinct values of $k$ modulo $t$.
We apply this result to studying an analogue of the power generator
over an elliptic curve. These results are elliptic curve analogues
of those obtained for multiplicative groups of finite fields and
residue rings.
Categories:11L07, 11T23, 11T71, 14H52, 94A60 

2. CJM 2001 (vol 53 pp. 212)
 Puppe, V.

Group Actions and Codes
A $\mathbb{Z}_2$action with ``maximal number of isolated fixed
points'' ({\it i.e.}, with only isolated fixed points such that
$\dim_k (\oplus_i H^i(M;k)) =M^{\mathbb{Z}_2}, k = \mathbb{F}_2)$
on a $3$dimensional, closed manifold determines a binary selfdual
code of length $=M^{\mathbb{Z}_2}$. In turn this code determines
the cohomology algebra $H^*(M;k)$ and the equivariant cohomology
$H^*_{\mathbb{Z}_2}(M;k)$. Hence, from results on binary selfdual
codes one gets information about the cohomology type of $3$manifolds
which admit involutions with maximal number of isolated fixed points.
In particular, ``most'' cohomology types of closed $3$manifolds do
not admit such involutions. Generalizations of the above result are
possible in several directions, {\it e.g.}, one gets that ``most''
cohomology types (over $\mathbb{F}_2)$ of closed $3$manifolds do
not admit a nontrivial involution.
Keywords:Involutions, $3$manifolds, codes Categories:55M35, 57M60, 94B05, 05E20 
