Ponder This

April 2009

<<March April May>>

f(x) = ((((x ^* c₁) & c₂) ^* c₃) & c₄) % c₅, where
c₁ = (2⁷⁹²-1)/(2³³-1);
c₂ = (2⁸¹⁶-1)/(2³⁴-1);
c₃ = 1+2³⁴+2^3*34+2^4*34+2^8*34;
c₄ = (2¹⁰⁸⁸-1)/(2³⁴-1)
c₅ = 2³³-1;

We encoded a linear erasure code using O(1) operations, thanks to Eli Biham who gave us a simpler solution. A nice discussion on this issue can be found at http://www.brand.site.co.il/riddles/200902q.html (link resides outside of ibm.com) and the links from it.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com