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Linear Complexity of Periodically Repeated Random Sequences by Zong-Duo Dai and Jun-Hui Yang examines the behavior of the linear complexity of random binary sequences when they are repeated periodically. Linear complexity refers to the length of the shortest Linear Feedback Shift Register (LFSR) capable of generating a given sequence, which is an important concept in Cryptography and Information Theory. The paper builds on earlier work by Rainer A. Rueppel, who suggested that the expected linear complexity of periodically repeated random sequences is close to the period 𝑇 T. The authors derive mathematical bounds for the expected linear complexity and its variance for general values of the period. Their results provide theoretical confirmation that the expected linear complexity is indeed very close to the period length, supporting Rueppel’s earlier hypothesis.

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