2k-factorial design with 10 parameters

Hi,

I'd like to apply a 2^k factorial design with k=10 parameters. Obviously 
this results in a quite long term for the model equation due to the high 
number of combinations of parameters.

How can I specify the equation for the linear model (lm) without writing 
all combinations explicitly down by hand? Does a R command exist for 
this problematic?

Thanks for your help in advance,
Sven