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| On the GF(p) Linear Complexity of Hall's Sextic Sequences and Some Cyclotomic-Set-Based |
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Citation： |
Xianmang HE,Liqin HU,Dong LI.On the GF(p) Linear Complexity of Hall's Sextic Sequences and Some Cyclotomic-Set-Based[J].Chinese Annals of Mathematics B,2016,37(4):515~522 |
| Page view： 1794
Net amount： 1598 |
Authors： |
Xianmang HE; Liqin HU;Dong LI |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.61202007, U1509213), Top Priority of the
Discipline (Information and Communication Engineering) Open
Foundation of Zhejiang, the Postdoctoral Science Foundation
(No.2013M540323) and the Outstanding Doctoral Dissertation in
Nanjing University of Aeronautics and Astronautics (No.BCXJ
13-17). |
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| Abstract： |
Klapper (1994) showed that there exists a class of geometric
sequences with the maximal possible linear complexity when
considered as sequences over $GF(2)$, but these sequences have very
low linear complexities when considered as sequences over $GF(p)(p$ is an odd prime). This linear complexity of a binary sequence
when considered as a sequence over $GF(p)$ is called $GF(p)$
complexity. This indicates that the binary sequences with high
$GF(2)$ linear complexities are inadequate for security in the
practical application, while, their $GF(p)$ linear complexities are
also equally important, even when the only concern is with attacks
using the Berlekamp-Massey algorithm [Massey, J. L., Shift-register
synthesis and bch decoding, {\it IEEE Transactions on Information
Theory}, {\bf 15}(1), 1969, 122--127]. From this perspective, in
this paper the authors study the $GF(p)$ linear complexity of Hall's
sextic residue sequences and some known cyclotomic-set-based
sequences. |
Keywords： |
Linear complexity, Hall's sextic residues sequence, Cyclotomic set |
Classification： |
94A60, 14G50, 68P25 |
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