User:Qed

Qed means Quod Erat Demonstrandum.

I maintain a couple websites worth visiting:

• My personal website [1]
• The Better String Library [2]

Pay no attention to the below. I have no idea where else to put a library of "editing tricks for Wikipedia".

Implementation tricks

When developing algorithms for Galois field computation on small Galois fields, a common performance optimization approach is to find a generator g and use the identity:

$ab=g^{\log _{g}(ab)}=g^{\log _{g}(a)+\log _{g}(b)}$

to implement multiplication as a sequence of table look ups for the log_g(x) and g^(x) functions and an integer addition operation. This exploits the property that all finite fields contain generators. In the Rijndael field example, the polynomial x + 1 (or {03}) is one such generator, since it is irreducible.