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This work studies the linear complexity of periodically repeated random sequences, extending prior results by R. Rueppel. It derives bounds for the expected linear complexity and its variance for sequences of arbitrary period 𝑇 T, and estimates the probability distribution of the sequence complexity. The study formally confirms Rueppel’s suggestion that the expected linear complexity is close to the period 𝑇 T, providing rigorous quantitative results for both general and extreme cases.

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245: $a: Linear Complexity of Periodically Repeated Random Sequences
245: $b:
082: $a:
100: $a: Zong-Duo Dai & Jun-Hui Yang
650: $a: Linear complexity of sequences
250: $a:
440: $v:
250: $b: Springer Verlag
250: $c: 1990
020: $a:
300: $a: 8