28 Mar
2016
28 Mar
'16
1:22 a.m.
* Warren D Smith <warren.wds@gmail.com> [Mar 28. 2016 09:10]:
18 different 32-bit generators each with period 2^32-1, consisting of all nonzero words [...]
How to find these: All the above generators are linear transformations of vectors over the 2-element field GF(2) and the period is the order of the linear transformation. By fast matrix powering over GF(2) you verify (for a good parameter choice) that no divisor of 2^wordsize-1 is the period, but 2^wordsize-1 is. Bad parameter choices that do not pass that test are discarded.
Computationalist's remark: replace "divisor" with "prime divisor". It might be interesting to look at the (primitive) polynomials that correspond to the maps. Best regards, jj
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