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On the k -Error Linear Complexity of p^{m} -Periodic Binary Sequences

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3 Author(s)
Yun Kyoung Han ; Pohang Univ. of Sci. & Technol. (POSTECH), Pohang ; Jin-Ho Chung ; Kyeongcheol Yang

In this correspondence, we study the statistical stability properties of pm -periodic binary sequences in terms of their linear complexity and k-error linear complexity, where p is n prime number and 2 is a primitive root modulo p2. We show that their linear complexity and k-error linear complexity take a value only from some specific ranges. We then present the minimum value k for which the k-error linear complexity is strictly less than the linear complexity in a new viewpoint different from the approach by Meidl. We also derive the distribution of pm-periodic binary sequences with specific k-error linear complexity. Finally, we get an explicit formula for the expectation value of the k-error linear complexity and give its lower and upper bounds, when k les [p/2].

Published in:

IEEE Transactions on Information Theory  (Volume:53 ,  Issue: 6 )