A~family of sequences over the $8$-element ring with low correlation
Matematičeskie voprosy kriptografii, Tome 1 (2010), pp. 85-109.

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

We construct a family of sequences over the 8-element ring with period $2^m-1$ such that their cross-correlation functions are asymptotically optimal with respect to the Sidel'nikov and Welch bounds
@article{MVK_2010_1_a4,
     author = {V. L. Kurakin},
     title = {A~family of sequences over the $8$-element ring with low correlation},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {85--109},
     publisher = {mathdoc},
     volume = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2010_1_a4/}
}
TY  - JOUR
AU  - V. L. Kurakin
TI  - A~family of sequences over the $8$-element ring with low correlation
JO  - Matematičeskie voprosy kriptografii
PY  - 2010
SP  - 85
EP  - 109
VL  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MVK_2010_1_a4/
LA  - ru
ID  - MVK_2010_1_a4
ER  - 
%0 Journal Article
%A V. L. Kurakin
%T A~family of sequences over the $8$-element ring with low correlation
%J Matematičeskie voprosy kriptografii
%D 2010
%P 85-109
%V 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MVK_2010_1_a4/
%G ru
%F MVK_2010_1_a4
V. L. Kurakin. A~family of sequences over the $8$-element ring with low correlation. Matematičeskie voprosy kriptografii, Tome 1 (2010), pp. 85-109. http://geodesic.mathdoc.fr/item/MVK_2010_1_a4/

[1] Kuzmin A. S., Kurakin V. L., Nechaev A. A., “Statisticheskie svoistva lineinykh rekurrent nad koltsami Galua i kvazifrobeniusovymi modulyami kharakteristiki 4”, Trudy po diskretnoi matematike, 4, FIZMATLIT, M., 2001, 91–128

[2] Nechaev A. A., Kuzmin A. S., Kurakin V. L., “Strukturnye, analiticheskie i statisticheskie svoistva lineinykh i polilineinykh rekurrent”, Trudy po diskretnoi matematike, 3, FIZMATLIT, M., 2000, 155–194

[3] Nechaev A. A., Kuzmin A. S., Kurakin V. L., “Vpolne ravnomernye lineinye rekurrenty nad koltsami Galua i QF-modulyami kharakteristiki 4”, Trudy po diskretnoi matematike, 5, FIZMATLIT, M., 2002, 103–158

[4] Nechaev A. A., “Kod Kerdoka v tsiklicheskoi forme”, Diskretnaya matematika, 1:4 (1989), 123–139 | MR | Zbl

[5] Nechaev A. A., “Konechnye kvazifrobeniusovy moduli, prilozheniya k kodam i lineinym rekurrentam”, Fundam. i Prikl. Matem., 1:1 (1995), 229–254 | MR | Zbl

[6] Sidelnikov V. M., “O vzaimnoi korrelyatsii posledovatelnostei”, Doklady AN SSSR, 196 (1971), 531–534 | MR

[7] Boztas S., Hammons R., Kumar P. V., “4-phase sequences with near-optimum correlation properties”, IEEE Trans. Inform. Theory, 38:3 (1992), 1101–1113 | DOI | Zbl

[8] McDonald B. R., Finite rings with identity, Dekker, New York, 1974 | MR | Zbl

[9] Nechaev A. A., “Finite rings with applications”, Handbook of Algebra, 5, eds. M. Hazewinkel, Elsevier, 2008, 213–320 | MR | Zbl

[10] Welch L. R., “Lower bounds on the maximum cross correlation of signals”, IEEE Trans. Inform. Theory, 20:3 (1974), 397–399 | DOI | MR | Zbl