Geodesic
On the linear complexity of binary sequences on the basis of biquadratic and sextic residue classes
Diskretnaya Matematika, Tome 22 (2010) no. 1, pp. 74-82 
V. A. Edemskii. On the linear complexity of binary sequences on the basis of biquadratic and sextic residue classes. Diskretnaya Matematika, Tome 22 (2010) no. 1, pp. 74-82. http://geodesic.mathdoc.fr/item/DM_2010_22_1_a5/
@article{DM_2010_22_1_a5,
     author = {V. A. Edemskii},
     title = {On the linear complexity of binary sequences on the basis of biquadratic and sextic residue classes},
     journal = {Diskretnaya Matematika},
     pages = {74--82},
     year = {2010},
     volume = {22},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2010_22_1_a5/}
}
TY  - JOUR
AU  - V. A. Edemskii
TI  - On the linear complexity of binary sequences on the basis of biquadratic and sextic residue classes
JO  - Diskretnaya Matematika
PY  - 2010
SP  - 74
EP  - 82
VL  - 22
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DM_2010_22_1_a5/
LA  - ru
ID  - DM_2010_22_1_a5
ER  - 
%0 Journal Article
%A V. A. Edemskii
%T On the linear complexity of binary sequences on the basis of biquadratic and sextic residue classes
%J Diskretnaya Matematika
%D 2010
%P 74-82
%V 22
%N 1
%U http://geodesic.mathdoc.fr/item/DM_2010_22_1_a5/
%G ru
%F DM_2010_22_1_a5

Voir la notice de l'article provenant de la source Math-Net.Ru

We suggest a method to compute the linear complexity of binary periodic sequences formed on the basis of biquadratic and sextic residue classes through the use of expansion of the sequence period into a sum of squares of integers. The values of the sequence polynomial are computed with the use of cyclotomic numbers of orders four and six.

[1] Lidl R., Niderraiter G., Konechnye polya, Mir, Moskva, 1988 | Zbl

[2] Ding C., Helleseth T., Shan W., “On the linear complexity of Legendre sequences”, IEEE Trans. Inf. Theory, 44:3 (1998), 1275–1278 | MR | Zbl

[3] Ding C., Helleseth T., Lam K. Y., “Several classes of binary sequences with tree-level autocorrelation”, IEEE Trans. Inf. Theory, 45 (1999), 2601–2606 | DOI | MR

[4] Kim J. H., Song H. Y., “On the linear complexity of Hall's sextic residue sequences”, IEEE Trans. Inf. Theory, 47 (2001), 2094–2096 | DOI | MR | Zbl

[5] Hall M., Combinatorial theory, Blaisdell, London, 1967 | MR | Zbl

[6] Whiteman A. L., “The cyclotomic numbers of order twelve”, Acta Arithmetica, 6 (1960), 53–76 | MR | Zbl

[7] Ireland K., Rosen M., A classical introduction to modern number theory, Springer, Berlin, 1982 | MR | Zbl

[8] Gantmakher V. E., Edemskii V. A., “Rezultaty sinteza dvoichnykh posledovatelnostei s kvaziodnourovnevoi avtokorrelyatsionnoi funktsiei, formiruemykh na osnove klassov vychetov po prostomu modulyu”, Izvestiya vuzov. Radioelektronika, 2007, no. 4, 14–23