Randomness quality of permuted pseudorandom binary sequences

This paper uses the DIEHARD statistical test suite to test the randomness quality of “permuted” versions of maximum length sequences generated by linear finite state machines (LFSM) such as cellular automata and linear feedback shift registers. Analysis shows that permuted sequences can be equivalently generated by using time-varying transformations derived from the original LFSM. Based on the above, we suggest the permuted transformation sequence scheme. Experimental results show that DIEHARD results are improved with respect to the original non-permuted sequences—up to seven more tests can be passed (total of 19 tests). Furthermore, a permutation vector is used to generate cyclically distinct permuted sequences and each sequence has a desirable maximum length period of 2n−1.