# non-overlapping template matching for bit sequences : why non-periodic templates?

To test a 'random' bit sequence for cryptographic strength I have been using the NIST's Non-overlapping Template Matching Test (See page 2-14 but I will explain here). This test uses a non-periodic bit template $B$ of length $m$ and counts the occurrences of the template in the bit sequence over $N$ blocks (where the blocks are just the original bit sequence split up into chunks). Then a Chi-squared test is done.

Let's say $B$ is $0001$, which is non-periodic.

If the bit sequence is $000010100010000...$ then we have...

    000010100010000...
0001                  no match
0001             no match
0001            no match
0001       no match.
...


Now the question is why should we particularly care about the distribution of non-periodic patterns as compared with periodic ones? Are they special in some way as related to random number generators?

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