A randomness test based on T-codes

In this paper, a new randomness test is proposed based on the T-complexity of a T-code, which is a variable-length self-synchronizing code introduced by Titchener in 1984. The proposed test can be used instead of the Lempel-Ziv compression test, which was removed from the NIST statistical test suite because the LZ-complexity has a defect such that its distribution of P-values is strictly discrete for random sequences of length 106. We show that T-complexity has almost ideal continuous distribution of P-values for the same sequences. In order to calculate T-complexity, a new T-decomposition algorithm is also proposed to realize forward parsing for a given sequence although the original T-decomposition uses backward parsing. Furthermore, it is shown that the proposed randomness test can detect undesirable pseudorandom numbers that the NIST statistical test suite cannot detect.