On the stability of periodic binary sequences with zone restriction

2019/03/28 by Su, Ming, Wang, Qiang
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1903.11968

Abstract

Traditional global stability measure for sequences is hard to determine because of large search space. We propose the k-error linear complexity with a zone restriction for measuring the local stability of sequences. Accordingly, we can efficiently determine the global stability by studying a local stability for these sequences. For several classes of sequences, we demonstrate that the k-error linear complexity is identical to the k-error linear complexity within a zone, while the length of a zone is much smaller than the whole period when the k-error linear complexity is large. These sequences have periods 2ⁿ, or 2^v r (r odd prime and 2 is primitive modulo r), or 2^v p₁^s₁ ⋯ p_n^s_n (p_i is an odd prime and 2 is primitive modulo p_i and p_i², where 1≤ i ≤ n) respectively. In particular, we completely determine the spectrum of 1-error linear complexity with any zone length for an arbitrary 2ⁿ-periodic binary sequence.

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