Linear complexity of transformed sequences

Abstract : This paper deals with the effect of bit change errors on the linear complexity of finite sequences. Though a change in a single bit can cause a large change in linear complexity, it is shown that on the average the change will be small even when many bits, e.g. 10 % are changed. General bijections and k-fold mappings on the set of sequences of length n are studied and tight bounds are found on the average difference in linear complexity between a sequence and its image. It is also shown that any mapping, on sequences of length n that take most sequences to images of low linear complexity must take many sequences to images that are far away from them in Hamming distance.
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Rapport
RR-1168, INRIA. 1990
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https://hal.inria.fr/inria-00075390
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H. Fell. Linear complexity of transformed sequences. RR-1168, INRIA. 1990. 〈inria-00075390〉

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