The properties of statistical procedures based on numbers of occurrences of aperiodic patterns in a random text are summarized. The asymptotic formulas for the expected value of the number of aperiodic words occurring a given number of times, and for the covariance matrix are given. The form of the optimal linear test based on these statistics is established.
block ciphers, distribution of $m$-patterns, efficacy, optimal linear test
and Volkovich, Z.
Testing Randomness via Aperiodic Words, Journal Of Statistical Planning And Inference, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=150566
(Accessed June 2, 2023)