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Journal of Applied Mathematics and Computing

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20-04-2016 | Original Research

On the linear complexity of Hall’s sextic residue sequences over \({ GF}(q)\)

Authors: Vladimir Edemskiy, Nikita Sokolovskiy

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2017

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Abstract

In this paper, we derive the linear complexity of Hall’s sextic residue sequences over the finite field of odd prime order. The order of the field is not equal to a period of the sequence. Our results show that Hall’s sextic residue sequences have high linear complexity over the finite field of odd order. Also we estimate the linear complexity of series of generalized sextic cyclotomic sequences. The linear complexity of these sequences is larger than half of the period.

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Title: On the linear complexity of Hall’s sextic residue sequences over
Authors: Vladimir Edemskiy
Nikita Sokolovskiy
Publication date: 20-04-2016
Publisher: Springer Berlin Heidelberg
Published in: Journal of Applied Mathematics and Computing / Issue 1-2/2017
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-016-1010-2

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