Whilst waiting for the survey to finish, I’ve been doing some work on maximum length sequences.
First what is a maximal length sequence? In practice they are an apparently random set of numbers all with an equal number of bits, n, such that the length of the sequence is 2^n or often 2^n – 1 (as sometimes one number such as all zeros might never change.)
So, let’s use a simple example where n is 2 so we get a two bit sequence with numbers 0 to 3 .The simplest sequence is that created by the rule that when we get to the maximum number we return to zero as in 0,1,2,3,0,1,2,3,0,1,2,3, etc. . But in general, we can specify any sequence by stating the rules underlying the sequence. If for example we have the following transformations:
00->10, 01 -> 11, 10 -> 01, and 11 ->00
we get the sequence:
00, 10, 01, 11, 00, 10, etc. Continue reading →