Geodesic
On the Hamming distance between binary representations of linear recurrent sequences over field $GF(2^k)$ and ring $\mathbb{Z}_{2^n}$
Matematičeskie voprosy kriptografii, Tome 7 (2016) no. 1, pp. 71-82 Cet article a éte moissonné depuis la source Math-Net.Ru

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Linear recurrent sequences over the field $GF(2^k)$ and over the ring $\mathbb{Z}_{2^n}$ with dependent recurrent relations are considered. We establish the bounds for the Hamming distance between two binary sequences obtained from the initial sequences by replacing each element by its image under the action of arbitrary maps into the field of two elements. 
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O. V. Kamlovskiy. On the Hamming distance between binary representations of linear recurrent sequences over field $GF(2^k)$ and ring $\mathbb{Z}_{2^n}$. Matematičeskie voprosy kriptografii, Tome 7 (2016) no. 1, pp. 71-82. http://geodesic.mathdoc.fr/item/MVK_2016_7_1_a3/

[1] Kuzmin A. S., Kurakin V. L., Nechaev A. A., “Psevdosluchainye i polilineinye posledovatelnosti”, Trudy po diskretnoi matematike, 1 (1997), 139–202 | MR | Zbl

[2] Nawaz Y., Gong G., “WG: a family of stream ciphers with designed randomness properties”, Information Sciences, 178:7 (2008), 1903–1916 | DOI | MR | Zbl

[3] Goltvanitsa M. A., Zaitsev S. N., Nechaev A. A., “Skruchennye lineinye rekurrenty maksimalnogo perioda nad koltsami Galua”, Fundam. i prikl. matematika, 17:3 (2012), 5–23 | MR | Zbl

[4] Golomb S. W., Gong G., Signal design for good correlation, New York, 2005, 438 pp. | MR

[5] Nechaev A. A., “Tsiklovye tipy lineinykh podstanovok nad konechnymi kommutativnymi koltsami”, Matem. sb., 184:3 (1993), 21–56 | MR | Zbl

[6] B. A. Pogorelov, V. N. Sachkov (red.), Slovar kriptograficheskikh terminov, MTsNMO, M., 2006, 92 pp.

[7] Logachev O. A., Salnikov A. A., Yaschenko V. V., Bulevy funktsii v teorii kodirovaniya i kriptologii, MTsNMO, M., 2012, 584 pp.

[8] Kamlovskii O. V., “Kolichestvo poyavlenii elementov v vykhodnykh posledovatelnostyakh filtruyuschikh generatorov”, Prikladnaya diskretnaya matematika, 2013, no. 3(21), 11–25

[9] Kamlovskii O. V., “Ravnomernye posledovatelnosti nad prostymi polyami, postroennye iz odnogo klassa lineinykh rekurrent nad koltsami vychetov”, Problemy peredachi informatsii, 50:2 (2014), 60–76 | MR | Zbl

[10] Kamlovskii O. V., Kuzmin A. S., “Otsenki chastot poyavleniya elementov v lineinykh rekurrentnykh posledovatelnostyakh nad koltsami Galua”, Fundam. i prikl. matematika, 6:4 (2000), 1083–1094 | MR | Zbl

[11] Kamlovskii O. V., “Metod trigonometricheskikh summ dlya issledovaniya chastot $r$-gramm v starshikh koordinatnykh posledovatelnostyakh lineinykh rekurrent nad koltsom $\mathbb{Z}_{2^n}$”, Matematicheskie voprosy kriptografii, 1:4 (2010), 33–62

[12] Bylkov D. N., “Ob odnom klasse bulevykh funktsii, postroennykh s ispolzovaniem starshikh razryadnykh posledovatelnostei lineinykh rekurrent”, Prikladnaya diskretnaya matematika. Prilozhenie, 7 (2014), 59–60