Z. Chen, Jakob Obrovsky, Arne Winterhof,
"Maximum-order Complexity and 2-Adic Complexity"
, in IEEE Transactions on Information Theory, Vol. 70, Nummer 8, Seite(n) 6060--6067, 2024, ISSN: 0018-9448
Original Titel:
Maximum-order Complexity and 2-Adic Complexity
Sprache des Titels:
Englisch
Original Kurzfassung:
The 2-adic complexity has been well-analyzed in the periodic case. However, we are not aware of any theoretical results in the aperiodic case. In particular, the Nth 2-adic complexity has not been studied for any promising candidate of a pseudorandom sequence of finite length N. Also nothing seems be known for a part of the period of length N of any cryptographically interesting periodic sequence. Here we introduce the first method for this aperiodic case. More precisely, we study the relation between Nth maximum-order complexity and Nth 2-adic complexity of binary sequences and prove a lower bound on the Nth 2-adic complexity in terms of the Nth maximum-order complexity. Then any known lower bound on the Nth maximum-order complexity implies a lower bound on the Nth 2-adic complexity of the same order of magnitude. In the periodic case, one can prove a slightly better result. The latter bound is sharp, which is illustrated by the maximum-order complexity of ell -sequences. The idea of the proof helps us to characterize the maximum-order complexity of periodic sequences in terms of the unique rational number defined by the sequence. We also show that a periodic sequence of maximal maximum-order complexity must be also of maximal 2-adic complexity.
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