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Linear complexity of a sequence obtained from a periodic sequence by either substituting, inserting, or deleting k symbols within one period

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3 Author(s)
Jiang, S. ; State Key Lab. of Inf. Security, Acad. Sinica, Beijing, China ; Zongduo Dai ; Imamura, K.

A unified derivation of the bounds of the linear complexity is given for a sequence obtained from a periodic sequence over GF(q) by either substituting, inserting, or deleting k symbols within one period. The lower bounds are useful in case of n<N/k, where N and n are the period and the linear complexity of the sequence, respectively. It is shown that all three different cases can be treated very simply in a unified manner. The bounds are useful enough to show how wide the distribution of the linear complexity becomes as k increases, although they are not always tight because their derivations do not use the information about the change values

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Information Theory, IEEE Transactions on  (Volume:46 ,  Issue: 3 )